Question

On a coordinate plane, 2 exponential functions are shown. Function f (x) approaches y = 0 in quadrant 2 and increases into quadrant 1. It crosses the y-axis at (0, 0.5) and goes through (1, 4). Function g (x) approaches y = 0 in quadrant 3 and decreases into quadrant 4. It crosses the y-axis at (0, negative 0.5) and goes through (1, negative 4).
Which function represents g(x), a reflection of f(x) = Two-fifths (10)x across the x-axis?

g(x) = Negative two-fifths(10)x
g(x) = Negative two-fifths (one-tenth) Superscript x
g(x) = Two-fifths (one-tenth) Superscript negative x
g(x) = Two-fifths(10)-x

Answer 1

Reflection across the x-axis multiplies the function by −1. So g(x) = −f(x) = −(2/5)·10^x.

(That gives g(1) = −4 and g(0) = −2/5 ≈ −0.4.)