Question

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

The table displays pairs of input-output for the function f(x).
x
f(x)

0
−3

1
6

2
−9


Table 2

x
g(x)

0

1

2

Answer 1

A horizontal transformation with k = 1/2 means g(x) = f((1/2)x) = f(x/2).

Compute:
- g(0) = f(0) = −3
- g(1) = f(1/2) = −12(1/4) + 21(1/2) − 3 = −3 + 10.5 − 3 = 9/2 (4.5)
- g(2) = f(1) = 6

So Table 2:
x: 0 → g(x) = −3
x: 1 → g(x) = 9/2
x: 2 → g(x) = 6