On a coordinate plane, 2 exponential functions are shown. f (x) decreases from quadrant 2 to quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 4) and goes through (1, 2). g (x) increases from quadrant 3 into quadrant 4 and approaches y = 0. It crosses the y-axis at (0, negative 4) and goes through (1, negative 2).

Which function represents g (x), a reflection of f (x) = 4 (one-half) Superscript x across the x-axis?

g (x) = - 4 (2) x

g (x) = 4 (2) - x

g (x) = - 4 (one-half) Superscript x

Question

Mathematics

Alfredo Camacho

26 November, 06:47

On a coordinate plane, 2 exponential functions are shown. f (x) decreases from quadrant 2 to quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 4) and goes through (1, 2). g (x) increases from quadrant 3 into quadrant 4 and approaches y = 0. It crosses the y-axis at (0, negative 4) and goes through (1, negative 2).

Which function represents g (x), a reflection of f (x) = 4 (one-half) Superscript x across the x-axis?

g (x) = - 4 (2) x

g (x) = 4 (2) - x

g (x) = - 4 (one-half) Superscript x

+5

Answers (1)

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Hermione · Answer 1

g (x) = - 4 (one-half) Superscript x

Step-by-step explanation:

We want to reflex the function: f (x) = 4 (1/2) ^x across x-axis.

Reflection across x-axis is obtained multiplying parent function by minus one.

Therefore, the reflection of the function is: - f (x) = - 4 (1/2) ^x = g (x)