Functions and Graphs: Increasing, Decreasing, and Composition Quiz

1. When identifying the intervals for increasing, decreasing, and constant, which variables do we focus on?

Neither x's nor y's as intervals can be determined without focusing on any specific variable

Both x's and y's because they both provide equal information for intervals

The x's
because we are looking from left to right
mark the changes on the x-axis

The y's because we are looking from bottom to top and mark the changes on the y-axis

When identifying intervals for increasing, decreasing, and constant, we focus on the x's because we observe changes from left to right on the x-axis. The y-axis is used to represent the function's output, while x-axis represents its input which helps determine the function's behavior.

Explanation

When identifying intervals for increasing, decreasing, and constant, we focus on the x's because we observe changes from left to right on the x-axis. The y-axis is used to represent the function's output, while x-axis represents its input which helps determine the function's behavior.

2. When is a graph increasing?

The picture is falling (as you move from left to right).

The picture is waving (moves up and down randomly as you move from left to right).

The picture is rising (as you move from left to right)

The picture is constant (does not change as you move from left to right).

In mathematics, a graph is considered increasing when the curve is rising or moving upwards as you move from left to right. This indicates growth or positive change in the values represented by the graph.

Explanation

In mathematics, a graph is considered increasing when the curve is rising or moving upwards as you move from left to right. This indicates growth or positive change in the values represented by the graph.

3. When is a graph decreasing?

The graph is moving downwards

The graph is moving upwards

The graph is staying constant

The picture is "falling" (as you move from left to right)

In mathematics, a graph is considered decreasing when the plotted line or curve is falling from left to right. This indicates a decrease in the dependent variable as the independent variable increases.

Explanation

In mathematics, a graph is considered decreasing when the plotted line or curve is falling from left to right. This indicates a decrease in the dependent variable as the independent variable increases.

4. What is the correct sentence for Relative Maximum/Minimum?

Determining the slope of a tangent line at a critical point.

Absolute peak of a function at a given x-coordinate.

Maximize/minimize the function at a specific point.

Relative (maximum/minimum) of (y-value) when x = (x value)

The correct sentence structure for expressing Relative Maximum/Minimum includes specifying the type (maximum/minimum), the y-value, and the x-value at which it occurs.

Explanation

The correct sentence structure for expressing Relative Maximum/Minimum includes specifying the type (maximum/minimum), the y-value, and the x-value at which it occurs.

5. What is a relative maximum?

The point with the smallest value in a region

The lowest point in a region (a valley)

The midpoint in a region

The highest point in a region. (a hill)

A relative maximum is defined as the highest point in a region, similar to the peak of a hill. It is not the lowest point (valley), midpoint, or the point with the smallest value.

Explanation

A relative maximum is defined as the highest point in a region, similar to the peak of a hill. It is not the lowest point (valley), midpoint, or the point with the smallest value.

6. What is a relative minimum?

A point of intersection between two lines

An average value within a dataset

The lowest point in a region. (a valley)

The highest point in a region (a mountain)

A relative minimum refers to the lowest point within a specific region or interval. It is not necessarily the overall lowest point in the entire dataset or graph, but rather the lowest point within a local area.

Explanation

A relative minimum refers to the lowest point within a specific region or interval. It is not necessarily the overall lowest point in the entire dataset or graph, but rather the lowest point within a local area.

7. What is the equation of the graph represented by a straight line passing through the origin?

Y = x

Y = x + 1

Y = 2x

Y = -x

The correct equation for a straight line passing through the origin is y = mx, where m is the slope. In this case, m = 1, so the equation is y = x.

Explanation

The correct equation for a straight line passing through the origin is y = mx, where m is the slope. In this case, m = 1, so the equation is y = x.

8. What is the equation for the graph of a parabola?

Y = x + 3

Y = 3x^2

Y = 2x

Y = x2

The correct equation for a parabola is in the form y = ax^2, where 'a' is a constant coefficient determining the direction and width of the parabola. This equation represents a symmetrical curve that opens upwards or downwards.

Explanation

The correct equation for a parabola is in the form y = ax^2, where 'a' is a constant coefficient determining the direction and width of the parabola. This equation represents a symmetrical curve that opens upwards or downwards.

9. What is the equation of the graph shown?

Y = x^2

Y = 1/x

Y = x + 1

Y = /x (square root of x)

The correct equation for the graph is y = √x, where y represents the square root of x. The other options do not represent the graph shown accurately.

Explanation

The correct equation for the graph is y = √x, where y represents the square root of x. The other options do not represent the graph shown accurately.

10. What is the equation for the graph of a hyperbola?

Y = 2x + 3

Y = x^2

Y = 1/x

Y = √x

The correct equation for a hyperbola is y = 1/x, as it represents the inverse variation relationship between x and y values. The incorrect options do not correspond to the characteristics of a hyperbola graph.

Explanation

The correct equation for a hyperbola is y = 1/x, as it represents the inverse variation relationship between x and y values. The incorrect options do not correspond to the characteristics of a hyperbola graph.

11. How do you find the solution for (f g) (#) when is addition, subtraction, multiplication, or division?

Combine f and g without performing any operation to get the final solution.

Divide f by g and find the remainder for division operation.

Find f(#)
Find g(#)
Then perform the operation <> on the two answer

Perform the operation on f and g without finding the individual answers.

To find the solution for (f g) (#), it is essential to find f(#) and g(#) before performing the specified operation on the two obtained answers. This step-wise approach ensures accurate calculation based on the given operations.

Explanation

To find the solution for (f g) (#), it is essential to find f(#) and g(#) before performing the specified operation on the two obtained answers. This step-wise approach ensures accurate calculation based on the given operations.

12. How is the domain of f/g different from f+g, f-g, or fg?

The domain of f/g is the product of the domains of f and g.

The domain of f/g is the intersection of the domains of f and g.

The domain of f/g is the sum of the domains of f and g.

The domain if f/g is the domain of the others minus all the numbers where g(x) = 0.

The domain of a fraction f/g excludes any numbers where the denominator g is equal to 0 to avoid division by zero errors. This restriction does not apply to addition, subtraction, or multiplication of functions.

Explanation

The domain of a fraction f/g excludes any numbers where the denominator g is equal to 0 to avoid division by zero errors. This restriction does not apply to addition, subtraction, or multiplication of functions.

13. How do you evaluate (fog)(#)?

Substitute g(#) into f first and then find the resulting value.

Find g(#).
Then plug the answer from above into f.
The answer from the second step is the answer to the question.

Evaluate f(#) first and then find g(#) to get the final answer.

Multiply f(#) by g(#) to obtain the result.

When evaluating (fog)(#), you need to find g(#) first and then substitute that value into f to obtain the answer. This involves finding the composition of the two functions in the correct order.

Explanation

When evaluating (fog)(#), you need to find g(#) first and then substitute that value into f to obtain the answer. This involves finding the composition of the two functions in the correct order.