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=23x−1

B.y=x+5

C.y=52x+6

D.y=0.75x−9

E.y=4x−2


A vertical stretch occurs when the graph of a function is stretched away from the x-axis. Mathematically, this happens when the coefficient of \(x\) is multiplied by a factor greater than 1. A vertical compression, on the other hand, happens when this coefficient is multiplied by a factor between 0 and 1.

The parent function given is \( f(x) = x \), and to vertically stretch the function, we multiply \(x\) by a constant greater than 1.

Let's evaluate the choices:

- **A: \( y = 23x - 1 \)**  
  The coefficient of \(x\) is 23, which is greater than 1. Therefore, this represents a vertical stretch.

- **B: \( y = x + 5 \)**  
  The coefficient of \(x\) is 1, which does not result in a vertical stretch.

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

- **D: \( y = 0.75x - 9 \)**  
  The coefficient of \(x\) is 0.75, which is less than 1, so this represents a vertical compression.

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

### Correct Answers:  
- A: \( y = 23x - 1 \)
- C: \( y = \frac{5}{2}x + 6 \)

Would you like further clarification or details on vertical transformations?  
Here are some additional questions to expand your understanding:

1. What is the difference between a vertical stretch and a vertical compression?
2. How does adding or subtracting a constant (like in \( y = x + 5 \)) affect the graph of a function?
3. What is the effect of a negative coefficient on the transformation of a function?
4. How can you identify horizontal stretches or compressions in a function?
5. How would you graph a vertically stretched function like \( y = 4x \)?

**Tip**: Always look at the coefficient of \(x\) to determine whether a function is being stretched or compressed 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 = 23x - 1, B. y = x + 5, C. y = 5/2x + 6, D. y = 0.75x - 9, E. y = 4x - 2

Explore how to identify vertical stretches in function transformations. This problem involves transforming the parent function f(x) = x and recognizing vertical stretches in various equations. Perfect for students in Grades 9-10 looking to understand key transformation concepts.

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