Question

Use the tables to answer the question.

The function g(x)
is created by horizontally stretching the parent function, f(x)=−12x^2+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 _
1 _
2 _

Answer 1

To create the function \( g(x) \) by horizontally stretching the parent function \( f(x) = -12x^2 + 21x - 3 \) with a \( k \) factor of \( \frac{1}{2} \), we replace \( x \) in \( f(x) \) with \( 2x \). This is because a horizontal stretch by a factor of \( k \) means replacing \( x \) with \( kx \).

So, we have:
\[
g(x) = f(2x) = -12(2x)^2 + 21(2x) - 3
\]
Calculating this, we get:
\[
g(x) = -12 \cdot 4x^2 + 42x - 3 = -48x^2 + 42x - 3
\]

Next, we will calculate the values of \( g(x) \) for \( x = 0, 1, 2 \).

1. For \( x = 0 \):
\[
g(0) = -48(0)^2 + 42(0) - 3 = -3
\]

2. For \( x = 1 \):
\[
g(1) = -48(1)^2 + 42(1) - 3 = -48 + 42 - 3 = -9
\]

3. For \( x = 2 \):
\[
g(2) = -48(2)^2 + 42(2) - 3 = -48 \cdot 4 + 84 - 3 = -192 + 84 - 3 = -111
\]

Now we can fill in Table 2 for \( g(x) \):

**Table 2**

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

So, the complete Table 2 shows the values of \( g(x) \) at the appropriate \( x \) values.