Mrs. Marshall asked her students to transform the parent function f(x)=xf(x)=x by vertically stretching the function to create g(x)g(x). Which of the following represent a vertical stretch?

Select **TWO** correct answers.

A.y=23x−1y=23x−1

B.y=x+5y=x+5

C.y=52x+6y=52x+6

D.y=0.75x−9y=0.75x−9

E.y=4x−2y=4x−2


To identify the transformations that represent a vertical stretch of the parent function \( f(x) = x \), we need to focus on the coefficient of \( x \), which is the value that multiplies \( x \). A vertical stretch occurs when this coefficient is greater than 1 or less than -1 (i.e., its absolute value is greater than 1).

Let's analyze each option:

- **A. \( y = \frac{2}{3}x - 1 \)**: The coefficient of \( x \) is \( \frac{2}{3} \), which is less than 1. This represents a vertical **compression**, not a stretch.
  
- **B. \( y = x + 5 \)**: The coefficient of \( x \) is 1. This is the original parent function with a vertical shift, not a stretch.

- **C. \( y = \frac{5}{2}x + 6 \)**: The coefficient of \( x \) is \( \frac{5}{2} \), which is greater than 1. This represents a vertical **stretch**.

- **D. \( y = 0.75x - 9 \)**: The coefficient of \( x \) is 0.75, which is less than 1. This is a vertical **compression**, not a stretch.

- **E. \( y = 4x - 2 \)**: The coefficient of \( x \) is 4, which is greater than 1. This represents a vertical **stretch**.

Thus, the correct answers are:
- **C. \( y = \frac{5}{2}x + 6 \)**
- **E. \( y = 4x - 2 \)**

### Would you like more details or have any further questions?

Here are five related questions to deepen understanding:
1. What is the difference between vertical stretching and compression?
2. How do vertical shifts affect the graph of a function?
3. Can you describe a horizontal stretch, and how does it differ from vertical stretching?
4. How does the transformation \( y = -kx \) differ from \( y = kx \) in terms of graph behavior?
5. What happens to the graph if a negative coefficient is used for \( x \) (e.g., \( y = -2x \))?

**Tip:** To recognize vertical stretching, always check the absolute value of the coefficient of \( x \). If it’s greater than 1, the graph stretches vertically.

Mrs. Marshall asked her students to transform the parent function f(x)=x by vertically stretching the function to create g(x). Which of the following represent a vertical stretch? Select TWO correct answers. A. y = 2/3x - 1 B. y = x + 5 C. y = 5/2x + 6 D. y = 0.75x - 9 E. y = 4x - 2

Learn how to identify vertical stretches in linear functions. This problem asks which transformations of the parent function f(x) = x result in a vertical stretch. The detailed solution explains how coefficients affect stretching or compressing. Suitable for students in Grades 8-10.

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