Question

The function f(x) = 8(one-fourth) Superscript x is reflected across the y-axis to create g(x). Which table of values could be used to graph g(x)?

A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entires 128, 32, 8, 2, one-half. The third column is labeled g (x) with entries one-half, 2, 8, 32, 128.
A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entires 128, 32, 0, 2, one-half. The third column is labeled g (x) with entries one-half, 2, 0, 32, 128.
A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entires 128, 32, 8, 2, one-half. The third column is labeled g (x) with entries negative 128, negative 32, negative 8, negative 2, negative one-half.
A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entires 128, 32, 0, 2, one-half. The third column is labeled g (x) with entries negative 128, negative 32, 0, negative 2, negative one-half.

Answer 1

Reflection across the y-axis gives g(x)=f(−x)=8(1/4)^(−x)=8·4^x.

Evaluate at x = −2, −1, 0, 1, 2:
- f: 128, 32, 8, 2, 1/2
- g: 1/2, 2, 8, 32, 128

So the first table (option A) is correct.