Question

Use the tables to answer the question.
The function g(x) is created by horizontally stretching the parent function, f(x)=−12x2+21x−3, with a k factor of 1/2. Complete the table to show how the function has changed. (1 point)

Table 1

| x | f(x) |
| 0 | -3 |
| 1 | 6 |
| 2 | -9 |

Table 2

| x | g(x) |
| 0 | -3 |
| 1 | ? |
| 2 | ? |

Answer 1

that is wrong

Answer 2

To find the values of \( g(x) \) for the function that has been horizontally stretched with a factor of \( k = \frac{1}{2} \), we need to replace \( x \) in the original function \( f(x) \) with \( \frac{x}{k} \). In this case, \( k = \frac{1}{2} \), so we'll replace \( x \) with \( 2x \) in \( f(x) \).

Given \( f(x) = -12x^2 + 21x - 3 \), we can express \( g(x) \) as:

\[
g(x) = f(2x) = -12(2x)^2 + 21(2x) - 3
\]

Now let's calculate \( g(x) \) for the values in Table 2:

1. **For \( x = 0 \)**:
\[
g(0) = f(2 \cdot 0) = f(0) = -3
\]

2. **For \( x = 1 \)**:
\[
g(1) = f(2 \cdot 1) = f(2) = -12(2)^2 + 21(2) - 3
\]
\[
= -12 \cdot 4 + 42 - 3
\]
\[
= -48 + 42 - 3
\]
\[
= -48 + 39
\]
\[
= -9
\]

3. **For \( x = 2 \)**:
\[
g(2) = f(2 \cdot 2) = f(4) = -12(4)^2 + 21(4) - 3
\]
\[
= -12 \cdot 16 + 84 - 3
\]
\[
= -192 + 84 - 3
\]
\[
= -192 + 81
\]
\[
= -111
\]

Now we can complete Table 2:

| x | g(x) |
|---|------|
| 0 | -3 |
| 1 | -9 |
| 2 | -111 |

Thus, the completed Table 2 is as follows:

| x | g(x) |
|---|-------|
| 0 | -3 |
| 1 | -9 |
| 2 | -111 |