Question

The graph represents the function f(x) = 10(2)x.

On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (negative 1, 5), (0, 10), (1, 20), (2, 40).
How would the graph change if the b value in the equation is decreased but remains greater than 1? Check all that apply.

The graph will begin at a lower point on the y-axis.
The graph will increase at a faster rate.
The graph will increase at a slower rate.
The y-values will continue to increase as x-increases.
The y-values will each be less than their corresponding x-values.

Answer 1

Correct choices:
- The graph will increase at a slower rate.
- The y-values will continue to increase as x increases.

Explanation in brief:
- The y-intercept y(0) = 10·b^0 = 10 is unchanged, so it does not "begin at a lower point on the y-axis."
- If 1 < b < 2 the function still grows (since b > 1) but grows more slowly than when b = 2, so it increases at a slower rate.
- The y-values remain increasing as x increases because b > 1.
- The statement that y-values are each less than their corresponding x-values is false (for example y(1) = 10b > 1).