Question

Two exponential functions are shown in the table.

A 3-column table has 5 rows. The first column is labeled x with entries 2, 1, 0, negative 1, negative 2. The second column is labeled f (x) = 2 Superscript x Baseline with entries 4, 2, 1, one-half, one-fourth. The third column is labeled g (x) = (one-half) superscript x Baseline with entries one-fourth, one-half, 1, 2, 4.
Which conclusion about f(x) and g(x) can be drawn from the table?

The functions f(x) and g(x) are reflections over the x-axis.
The functions f(x) and g(x) are reflections over the y-axis.
The function f(x) is a decreasing function, and g(x) is an increasing function.
The function f(x) has a greater initial value than g(x

Answer 1

Answer: The functions are reflections over the y-axis.

Reason: g(x) = (1/2)^x = 2^(−x) = f(−x), so g is f with the input negated — a reflection of f across the y-axis. (They are not reflections across the x-axis, f is not decreasing while g increasing, and f(0)=g(0)=1 so f does not have a greater initial value.)