Question

Which of the following table shows that y equals k f of x results in the parent function y = x + 4 being vertically stretched by k factor of 3
X012

Answer 1

To show that the transformation \( y = k f(x) \) results in the parent function \( y = x + 4 \) being vertically stretched by a factor of \( k = 3 \), we will first define the transformation correctly and then evaluate it for the given \( x \)-values.

The parent function is given as:

\[
f(x) = x + 4
\]

If we want to vertically stretch this function by a factor of \( k = 3 \), we will apply the transformation:

\[
y = k f(x) = 3 (x + 4)
\]

Next, we can simplify this expression:

\[
y = 3x + 12
\]

Now, we’ll compute the values of \( y \) for the provided \( x \)-values (0, 1, 2):

1. For \( x = 0 \):
\[
y = 3(0) + 12 = 12
\]

2. For \( x = 1 \):
\[
y = 3(1) + 12 = 3 + 12 = 15
\]

3. For \( x = 2 \):
\[
y = 3(2) + 12 = 6 + 12 = 18
\]

So, the resulting values can now be compiled into a table:

| \( x \) | \( y \) |
|:-----:|:-----:|
| 0 | 12 |
| 1 | 15 |
| 2 | 18 |

This table shows the transformed values for the function \( y = 3(x + 4) \) or \( y = 3x + 12 \), demonstrating that the function has been vertically stretched by a factor of 3.