Now, describe the transformation h(x) = g (÷). In this transformation the inputs are being multiplied by a factor of to stretch the original graph horizontally

Intermediate Algebra
19th Edition
ISBN:9780998625720
Author:Lynn Marecek
Publisher:Lynn Marecek
Chapter9: Quadratic Equations And Functions
Section9.7: Graph Quadratic Functions Using Transformations
Problem 9.119TI: Graph f(x)=x2+2x3 by using transformations.
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Given the equation, graph the following. 

Now, describe the transformation \( h(x) = g\left(\frac{x}{2}\right) \).

In this transformation, the inputs are being multiplied by a factor of 

**2**

to stretch the original graph horizontally.
Transcribed Image Text:Now, describe the transformation \( h(x) = g\left(\frac{x}{2}\right) \). In this transformation, the inputs are being multiplied by a factor of **2** to stretch the original graph horizontally.
The image displays a graph of a cubic function \( f(x) = -x^3 + 3x \).

### Explanation of the Graph

- The graph is set on a coordinate plane with the x-axis ranging from approximately -0.5 to 4.5 and the y-axis from -3 to 1.
- The function is represented by a red curve.
- The graph shows the turning points and behavior of the function as it goes through a local maximum and minimum.

### Key Points

- **Point A**: This point is marked on the downward slope of the curve. It lies approximately between x = 1 and x = 1.5 on the graph at around y = -1.
- **Point B**: This point is marked at the local minimum of the curve. It is located at x = 2 on the x-axis, and approximately at y = -2.
- The curve starts from the top left, goes downwards to a local minimum, and then rises again towards the top right.

This graph can be used to study the basic properties of cubic functions, such as turning points, symmetry, and intervals of increase and decrease.
Transcribed Image Text:The image displays a graph of a cubic function \( f(x) = -x^3 + 3x \). ### Explanation of the Graph - The graph is set on a coordinate plane with the x-axis ranging from approximately -0.5 to 4.5 and the y-axis from -3 to 1. - The function is represented by a red curve. - The graph shows the turning points and behavior of the function as it goes through a local maximum and minimum. ### Key Points - **Point A**: This point is marked on the downward slope of the curve. It lies approximately between x = 1 and x = 1.5 on the graph at around y = -1. - **Point B**: This point is marked at the local minimum of the curve. It is located at x = 2 on the x-axis, and approximately at y = -2. - The curve starts from the top left, goes downwards to a local minimum, and then rises again towards the top right. This graph can be used to study the basic properties of cubic functions, such as turning points, symmetry, and intervals of increase and decrease.
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