Question

Which graph is the result of reflecting f(x) = One-fourth(8)x across the y-axis and then across the x-axis?

On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and incresaes into quadrant 1. It goes through the y-axis at (0, 0.25) and goes through (1, 2).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 1 and increases in quadrant 2. It crosses the y-axis at (0, 0.25) and goes through (negative 1, 2).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It crosses the y-axis at (0, negative 0.25) and goes through (1, negative 2).
On a coordinate plane, an exponential funtion increases in quadrant 3 into quadrant 4 and approaches y = 0. It goes through (negative 1, negative 2) and crosses the y-axis at (0, negative 0.25).

Answer 1

f(x) = (1/4)·8^x has f(0)=1/4 and f(1)=2 (matches the first graph).

Reflect across the y-axis: replace x by −x
g(x) = (1/4)·8^(−x). This still has g(0)=1/4 and g(−1)=2 (matches the second graph).

Reflect g across the x-axis: multiply by −1
h(x) = −(1/4)·8^(−x). This gives h(0)=−1/4 and h(−1)=−2, and the curve increases from quadrant III into quadrant IV approaching y=0 from below.

Therefore the fourth graph (through (−1, −2) and (0, −0.25), increasing from Q3 into Q4 and approaching y=0) is the correct result.