Use the graphs of $f$f​  and  $h$h​  to describe the transformation from the graph of $f$f​  to the graph of  $h$h​ .

$f\left(x\right)=-x+1$f(x)=−x+1​

$h\left(x\right)=f\left(2x\right)$h(x)=f(2x)​

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.

The graph of  $h$h​  is a Response area of the graph of $f$f​  by a factor of Response area.

To describe the transformation from the graph of $ f(x) = -x + 1 $ to $ h(x) = f(2x) $:

1. The graph of $ h(x) $ is a **horizontal compression** of the graph of $ f(x) $.
2. The compression factor is by a factor of **$ \frac{1}{2} $**.

So, the complete statement would be:

- The graph of $ h(x) $ is a **horizontal compression** of the graph of $ f(x) $ by a factor of $ \frac{1}{2} $. 

Would you like a detailed explanation of this transformation?

Here are five related questions:
1. What happens to a function when it is vertically stretched or compressed?
2. How would the transformation change if $ h(x) = f(\frac{x}{2}) $?
3. What effect does a negative sign in $ h(x) = -f(x) $ have on the graph?
4. How do you determine the horizontal shift of a function?
5. What is the impact on the graph if $ h(x) = f(x) + c $ where $ c $ is a constant?

**Tip:** For horizontal transformations, multiplying $ x $ by a factor greater than 1 compresses the graph, while dividing $ x $ stretches it.

Use the graphs of $f$ and $h$ to describe the transformation from the graph of $f$ to the graph of $h$.

$f(x) = -x + 1$

$h(x) = f(2x)$

The graph of $h$ is a Response area of the graph of $f$ by a factor of Response area.

Understand how to transform the graph of f(x) = -x + 1 to h(x) = f(2x) by applying horizontal compression. This solution demonstrates the effect of multiplying the input by a factor, suitable for high school math students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation