5933 Non-linear Identifying Y=kxn

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Anthony Nunan
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This quiz tests your knowledge of the five different shapes that are formed using the general equation :
where n = 1, -1, 2, -2 or 3.

Questions and Answers
• 1.

What type of equation would match the graph above?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
C. Parabola
Explanation
The graph above represents a U-shaped curve, which is characteristic of a parabola. A parabola is a type of equation that can be represented by a quadratic function. It has the general form of y = ax^2 + bx + c, where a, b, and c are constants. The graph matches a parabola because it is symmetric about a vertical line, with a single vertex point at the bottom.

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• 2.

What type of equation would match the graph above?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
C. Parabola
Explanation
The graph shown in the question has a U-shape, which is a characteristic of a parabola. A parabola is a type of equation that represents a quadratic function. It has the general form of y = ax^2 + bx + c, where a, b, and c are constants. The graph of a parabola can open upwards or downwards, depending on the value of the coefficient a. In this case, since the graph opens upwards, it suggests that the equation matches a parabola.

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• 3.

What type of equation would match the graph above?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
C. Parabola
Explanation
The graph shown in the question resembles a U-shaped curve, which is characteristic of a parabola. A parabola is a type of equation that can be represented by a quadratic equation in the form of y = ax^2 + bx + c. The graph of a parabola can open upwards or downwards, depending on the coefficient of the x^2 term. Therefore, based on the shape of the graph, it can be concluded that the equation matching the graph is a parabola.

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• 4.

What type of equation would match the graph above?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
C. Parabola
Explanation
The graph shown in the question appears to be a U-shaped curve, which is characteristic of a parabola. A parabola is a type of equation that can be represented by a quadratic equation in the form of y = ax^2 + bx + c. It has a single curve and is symmetric about its vertex. Therefore, the correct answer is Parabola.

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• 5.

What type of equation would match the graph above?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
B. Hyperbola
Explanation
The graph shown does not have a constant rate of change, which eliminates linear and cubic equations. It also does not have a U-shaped or symmetric curve, ruling out parabola. The graph resembles two curved lines that are symmetric about the origin, suggesting a hyperbola. Therefore, the correct answer is hyperbola.

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• 6.

What type of equation would match the graph above?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
B. Hyperbola
Explanation
The graph shown in the question is a curve that consists of two branches that are symmetric about the origin. This shape is characteristic of a hyperbola. A hyperbola is a type of conic section that is defined as the set of all points in a plane, the difference of whose distances from two fixed points (called foci) is constant. Therefore, the correct answer is hyperbola.

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• 7.

What type of equation would match the graph above?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
B. Hyperbola
Explanation
The graph shown does not have a linear or parabolic shape, as it does not follow a straight line or a U-shaped curve. It also does not match the shape of a cubic equation, which typically has a more pronounced curve. However, the graph does resemble the shape of a hyperbola, which is a type of conic section that consists of two distinct curves that are symmetric to each other. Therefore, the correct answer is hyperbola.

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• 8.

What type of equation would match the graph above?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
B. Hyperbola
• 9.

What type of equation would match the graph above?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
A. Linear
Explanation
The graph shown in the question is a straight line, which is characteristic of a linear equation. A linear equation is a polynomial equation of degree 1, where the variables are raised to the power of 1. The equation represents a relationship between two variables that can be represented by a straight line on a graph. Therefore, the correct answer is linear.

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• 10.

What type of equation would match the graph above?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
A. Linear
Explanation
The given graph appears to be a straight line, which is characteristic of a linear equation. Linear equations have a constant rate of change and can be represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. Therefore, the correct answer is Linear.

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• 11.

What type of equation would match the graph above?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
A. Linear
Explanation
The graph above represents a straight line, which is characteristic of a linear equation. A linear equation is a polynomial equation of degree 1, where the variables are raised to the power of 1. The graph shows a constant rate of change, indicating a linear relationship between the variables. Therefore, the correct answer is Linear.

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• 12.

What type of equation would match the graph above?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
A. Linear
Explanation
The graph shown in the question is a straight line, which indicates a linear equation. A linear equation is a polynomial equation of degree 1, where the variables are raised to the power of 1 and there are no higher powers or products of variables. In this case, the graph represents a linear relationship between two variables, indicating that the equation is linear.

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• 13.

What type of equation would match the graph above?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
D. Truncus
Explanation
The given graph does not resemble the shape of a linear equation, which is a straight line. It also does not resemble the shape of a hyperbola or a parabola, which have distinct curves. The graph does not resemble the shape of a cubic equation either, as it does not have the characteristic "S" shape. However, the graph does resemble the shape of a truncus, which is a type of equation that has a straight line followed by a curve. Therefore, the correct answer is Truncus.

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• 14.

What type of equation would match the graph above?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
D. Truncus
• 15.

What type of equation would match the graph above?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
D. Truncus
• 16.

What type of equation would match the graph above?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
D. Truncus
• 17.

What type of equation would match the graph above?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
E. Cubic
Explanation
The graph shown in the question suggests that the equation that matches it is a cubic equation. A cubic equation is a polynomial equation of degree 3, which means it has the highest exponent of 3. The graph appears to have two turning points, which is a characteristic of cubic functions. Therefore, the correct answer is cubic.

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• 18.

What type of equation would match the graph above?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
E. Cubic
Explanation
The graph shown in the question does not resemble a straight line (linear), a hyperbola, a parabola, or a truncus. However, it does resemble a cubic graph, which is characterized by a curved shape with both positive and negative slopes. Therefore, the correct answer is cubic.

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• 19.

What type of equation would match the graph above?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
E. Cubic
Explanation
The graph shown in the question represents a curve that is not a straight line, nor does it have the shape of a hyperbola or a parabola. It also does not resemble the shape of a truncus. The only option left is a cubic equation, which is a type of equation that can produce a graph with the curved shape shown in the question.

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• 20.

What type of equation would match the graph above?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
E. Cubic
Explanation
The graph shown in the question appears to have a curve that is not a straight line, but rather has a gradual increase followed by a gradual decrease. This shape is characteristic of a cubic equation, which is a type of polynomial equation with a degree of 3. In a cubic equation, the highest power of the variable is 3, and the graph typically exhibits this type of curve. Therefore, the correct answer is cubic.

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• 21.

What type of graph will the equation above generate?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
A. Linear
Explanation
The equation will generate a linear graph because the equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept. In a linear graph, the relationship between the x and y variables is a straight line.

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• 22.

What type of graph will the equation above generate?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
A. Linear
Explanation
The given equation will generate a linear graph. A linear graph represents a straight line and is characterized by a constant rate of change between the variables in the equation. In this case, the equation will generate a straight line when plotted on a graph.

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• 23.

What type of graph will the equation above generate?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
A. Linear
Explanation
The equation will generate a linear graph because a linear equation represents a straight line on a graph.

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• 24.

What type of graph will the equation above generate?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
A. Linear
Explanation
The given equation will generate a linear graph. A linear graph is a straight line that represents a linear relationship between two variables. The equation may be in the form of y = mx + b, where m is the slope of the line and b is the y-intercept. In a linear graph, the values of y increase or decrease at a constant rate as x changes.

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• 25.

What type of graph will the equation above generate?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
B. Hyperbola
Explanation
The given equation will generate a hyperbola. A hyperbola is a type of conic section that consists of two distinct curves that are mirror images of each other. The equation of a hyperbola typically involves terms with both x and y variables, and it has a specific pattern that distinguishes it from other types of graphs.

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• 26.

What type of graph will the equation above generate?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
B. Hyperbola
Explanation
The given equation will generate a hyperbola. A hyperbola is a type of conic section that consists of two separate curves, each resembling a mirrored "U" shape. The equation of a hyperbola typically involves terms with both x and y, resulting in a graph that is symmetrical along both the x-axis and y-axis.

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• 27.

What type of graph will the equation above generate?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
B. Hyperbola
• 28.

What type of graph will the equation above generate?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
B. Hyperbola
• 29.

What type of graph will the equation above generate?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
D. Truncus
Explanation
The term "truncus" is not a commonly used term in mathematics or graph theory. Therefore, it is likely that this question is incomplete or contains a typographical error. Without further information or context, it is not possible to determine what type of graph the equation will generate.

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• 30.

What type of graph will the equation above generate?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
D. Truncus
• 31.

What type of graph will the equation above generate?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
D. Truncus
Explanation
The given equation will generate a Truncus graph.

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• 32.

What type of graph will the equation above generate?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
D. Truncus
• 33.

What type of graph will the equation above generate?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
C. Parabola
Explanation
The equation mentioned in the question will generate a parabola. A parabola is a U-shaped curve that can open upwards or downwards, depending on the coefficients of the equation. The equation mentioned does not specify the coefficients, but regardless of their values, it will always result in a parabolic graph.

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• 34.

What type of graph will the equation above generate?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
C. Parabola
• 35.

What type of graph will the equation above generate?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
C. Parabola
Explanation
The given equation will generate a parabola. A parabola is a U-shaped curve that can open upwards or downwards. The equation of a parabola is typically in the form of y = ax^2 + bx + c, where a, b, and c are constants. The given question does not provide the equation, but it states that the equation will generate a parabola. Therefore, the correct answer is Parabola.

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• 36.

What type of graph will the equation above generate?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
C. Parabola
Explanation
The equation will generate a parabola because the graph of a parabola is represented by a quadratic equation. The equation given is not provided, but since the answer is "parabola," it can be inferred that the equation is a quadratic equation. The graph of a parabola is U-shaped and can open upwards or downwards, depending on the coefficients of the quadratic equation.

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• 37.

What type of graph will the equation above generate?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
E. Cubic
Explanation
The equation mentioned in the question will generate a cubic graph. A cubic graph is a type of graph that represents a cubic function, which is a polynomial function of degree three. In a cubic graph, the curve can have up to two turning points and can either be increasing or decreasing. The equation mentioned in the question is likely a cubic equation, which when graphed, will result in a cubic graph.

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• 38.

What type of graph will the equation above generate?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
E. Cubic
Explanation
The equation mentioned in the question will generate a cubic graph. A cubic graph is a type of polynomial graph with a degree of 3. It is characterized by its S-shaped curve, which can either be concave up or concave down. The equation provided is likely a cubic equation, which when graphed, will exhibit the characteristics of a cubic graph.

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• 39.

What type of graph will the equation above generate?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
E. Cubic
Explanation
The given equation will generate a cubic graph. A cubic graph is a type of polynomial graph that has a degree of 3. It is characterized by its S-shaped curve and can have multiple x-intercepts and turning points. The equation provided does not specify the actual equation, but since it is described as cubic, it suggests that the equation will have a variable raised to the power of 3.

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• 40.

What type of graph will the equation above generate?

• A.

Linear

• B.

Hyperbola

• C.

Parabola

• D.

Truncus

• E.

Cubic

Correct Answer
E. Cubic
Explanation
The equation mentioned in the question will generate a cubic graph. A cubic graph is a type of graph where the highest power of the variable is 3. It typically has a curved shape and can have multiple x-intercepts and turning points. The equation mentioned in the question is not provided, but since the answer is "Cubic," it can be inferred that the equation is a cubic equation.

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• 41.