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: B

Explanation:

Answer 2

B. The functions f(x) and g(x) are reflections over the y-axis.

Explanation:

From the information given the table appears as;

x f(x)=2^x g(x)=0.5^x

2 4 0.25

1 2 0.5

0 1 1

-1 0.5 2

-2 0.25 4

Plotting the two graphs to view the trends;

In the graph of f(x)=2^x against x you notice a curve with increasing positive slope.

In the graph of g(x)=0.5^x against x you notice a curve with a negative slope that is increasing.

In combining both graphs you notice that f(x) and g(x) are reflections over the y-axis.

Correct answer is ;The functions f(x) and g(x) are reflections over the y-axis.