Question

If the solid line models the function f(x) = |x2|
, what is the equation of the transformed function (dotted line) which vertically stretched the starting function by a factor of 3?



(1 point)
Responses

f(x) = x2−3
f(x) = x2−3

f(x) = x2+3
f(x) = x2+3

f(x) = 3|x2|
f(x) = 3|x2|

f(x) = |(x+3)2|
f(x) = |(x+3)2|
Question 2
9.

Identify the factor k that would cause the vertical compression (solid line) to the dilated function (the dotted line). Note: It might be helpful to notice a point on the dilated function and find the corresponding point on the original function to help determine the value of k.



(1 point)
Answer should be a whole number or a simplified fraction (no decimals).

k=

Answer 1

To answer the first question, we start with the function \( f(x) = |x^2| \). To stretch the function vertically by a factor of 3, we multiply the entire function by 3. The equation of the transformed function will be:

\[
f(x) = 3|x^2|
\]

So the correct response is:

**f(x) = 3|x^2|**

---

For the second question, if we have the dotted line representing a vertically stretched function, \( g(x) = 3|x^2| \), and we want to find the factor \( k \) that would cause a vertical compression back to the original function \( f(x) = |x^2| \), we can express that as:

\[
f(x) = k \cdot g(x)
\]

Given that \( g(x) = 3|x^2| \) and the original function \( f(x) = |x^2| \):

Setting them equal:

\[
|x^2| = k \cdot (3|x^2|)
\]

To find \( k \):

\[
k \cdot 3|x^2| = |x^2| \Rightarrow k = \frac{|x^2|}{3|x^2|}
\]

For \( |x^2| \neq 0 \):

\[
k = \frac{1}{3}
\]

So the answer for \( k \) is:

**k = \(\frac{1}{3}\)**