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 12
. 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



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Answer 1

A horizontal stretch by factor k = 12 gives g(x) = f(x/12). So

g(x) = f(x/12) = -12(x/12)^2 + 21(x/12) - 3 = -(1/12)x^2 + (7/4)x - 3.

Now evaluate:

- g(0) = -3
- g(1) = -(1/12) + 7/4 - 3 = -4/3
- g(2) = -(4/12) + 7/2 - 3 = 1/6

Table 2:
x: 0 → g(x) = -3; 1 → -4/3; 2 → 1/6.