Question

The graph of f(x) = One-half(2.5)x and its reflection across the x-axis, g(x), are shown.

On a coordinate plane, 2 exponential functions are shown. f (x) approaches y = 0 in quadrant 2 and then increases into quadrant 1. It crosses the y-axis at (0, 0.5) and goes through (2, 3). 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 (2, negative 3).

What is the range of g(x)?

all real numbers
all real numbers less than 0
all real numbers greater than 0
all real numbers less than or equal to 0

Answer 1

g(x) is the reflection of f(x) across the x-axis, so g(x) = -½(2.5)^x. That is always negative and approaches 0 but never reaches it.

Range: all real numbers less than 0.