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In mathematics, a “parent” function is the simplest function of a family of functions, which preserves the family's definition. In a sense, it is like the control of a function, something with which to compare any other results you acquire from the same function type. Let’s take a look at some examples, should we? See how much you know about them in this quiz!
Questions and Answers
1.
What does a linear function graph look like?
A.
B.
C.
D.
Correct Answer
A.
Explanation A linear function graph is a straight line that can be represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. The slope determines the steepness of the line, while the y-intercept is the point where the line crosses the y-axis. The graph of a linear function is always a straight line because the rate of change between the x and y variables is constant.
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2.
What does an absolute value graph look like?
A.
B.
C.
D.
Correct Answer
C.
Explanation An absolute value graph is a V-shaped graph that opens upwards or downwards depending on the coefficient of x. It is symmetric with respect to the y-axis and the vertex of the graph is at the origin (0,0). The graph represents the distance from zero, so it is always positive or zero.
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3.
What does a quadratic (Parabola) graph look like?
A.
B.
C.
D.
Correct Answer
B.
Explanation A quadratic graph, also known as a parabola, is a U-shaped curve. It is symmetric around a vertical line called the axis of symmetry. The vertex of the parabola is the highest or lowest point on the graph, depending on the direction it opens. The shape of the parabola can vary depending on the coefficients of the quadratic equation. If the coefficient of the x^2 term is positive, the parabola opens upwards, and if it is negative, the parabola opens downwards. The steepness of the curve is determined by the coefficient of the x^2 term.
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4.
What does a cubic graph look like?
A.
B.
C.
D.
Correct Answer
A.
Explanation A cubic graph is a type of graph that represents a cubic function. It is characterized by a curve that is either concave up or concave down, and it can have one or two points of inflection. The graph may also have a local maximum or minimum point, depending on the coefficients of the cubic function. Additionally, the graph can intersect the x-axis at one, two, or three points, depending on the roots of the cubic equation.
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5.
What does a rational graph look like?
A.
B.
C.
D.
Correct Answer
D.
Explanation A rational graph is a type of mathematical graph that represents a rational function. It typically consists of a curve or line with various branches and asymptotes. The graph may have vertical asymptotes where the function approaches infinity or negative infinity, and horizontal asymptotes where the function approaches a constant value as x approaches infinity or negative infinity. The graph may also have x-intercepts and y-intercepts, which represent points where the function crosses the x-axis or y-axis. Overall, a rational graph can have a variety of shapes and features depending on the specific rational function being represented.
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6.
What does a square root graph look like?
A.
B.
C.
D.
Correct Answer
C.
Explanation A square root graph is a curve that starts at the origin and gradually increases as the input values increase. The curve becomes steeper as the input values increase, but it never reaches negative values. The graph is symmetrical with respect to the y-axis and has a minimum point at the origin. As the input values approach positive infinity, the graph approaches positive infinity as well.
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7.
What is the formula of a linear graph?
A.
X3
B.
X2
C.
1/x
D.
F(x)=x
Correct Answer
D. F(x)=x
Explanation The formula of a linear graph is f(x) = x. This means that the value of y (represented by f(x)) is directly proportional to the value of x. As x increases or decreases, y will also increase or decrease in a straight line. This is the simplest form of a linear equation, where the slope of the line is equal to 1.
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8.
What is the formula of a absolute value graph?
A.
1/x
B.
|x|
C.
X2
D.
F(x)=x
Correct Answer
B. |x|
Explanation The formula for an absolute value graph is represented by |x|. This formula indicates that the graph of the function will be symmetrical around the y-axis, with the vertex at the origin (0,0). The absolute value function returns the distance of a number from zero, disregarding its sign. Therefore, when graphed, it will always result in a V-shaped graph.
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9.
What is the formula of a rational graph?
A.
1/x
B.
|x|
C.
X
D.
F(x)=x
Correct Answer
A. 1/x
Explanation The formula of a rational graph is 1/x. This is because a rational function is defined as the division of two polynomial functions. In this case, the numerator is a constant 1 and the denominator is x, resulting in the equation 1/x. This formula represents a graph that has a vertical asymptote at x = 0 and approaches zero as x approaches positive or negative infinity.
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10.
What is the formula of a cubic graph?
A.
1/x
B.
|x|
C.
X3
D.
F(x)=x
Correct Answer
C. X3
Explanation The formula of a cubic graph is represented by the equation f(x) = x^3. This equation indicates that the graph of the cubic function will have a shape similar to the letter "S" and will include points such as (0,0) and (-1,-1), (1,1), (-2,-8), (2,8), etc. The exponent of 3 in the equation indicates that the function is a cubic function, which means it has a degree of 3. Therefore, the correct answer is x^3.
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11.
What is the formula of a quadratic graph?
A.
X2
B.
X
C.
|x|
D.
1/x
Correct Answer
A. X2
Explanation The formula of a quadratic graph is x^2. This is because a quadratic equation is of the form ax^2 + bx + c, where a, b, and c are constants. In this case, since there are no other terms or constants given in the question, the formula of the quadratic graph is simply x^2.
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12.
What is the formula of a square root graph?
A.
1/x
B.
X
C.
|x|
D.
X2
Correct Answer
B. X
Explanation The formula for a square root graph is represented by the equation y = √x. In this equation, the variable x represents the input values, and the square root of x represents the corresponding output values, y. The graph of this equation will form a curve that starts from the origin (0,0) and gradually increases as x increases. The graph will never have negative y-values because the square root of a negative number is undefined. Therefore, the correct answer is X.
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13.
Fill in the blank.
This test was _________.
Correct Answer Challenging Easy Awesome
Explanation The given correct answer for this question is "Challenging, Easy, Awesome". This indicates that the test had a combination of different levels of difficulty. It may have started off challenging, then became easier, and finally ended on a positive note with an awesome experience.
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