Question

On a coordinate plane, an exponential function has a horizontal asymptote of y = 0. The function curves up into the first quadrant. It goes through (0, 3), (0.5, 5), (1, 10), (1.5, 23), (2, 50).
The given graph represents the function f(x) = 2(5)x. How will the appearance of the graph change if the a value in the function is decreased, but remains greater than 0?

The graph will increase at a slower rate.
The graph will show a decreasing, rather than increasing, function.
The graph will show an initial value that is lower on the y-axis.
The graph will increase at a constant additive rate, rather than a multiplicative rate.

Answer 1

Correct answer: The graph will show an initial value that is lower on the y-axis.

Explanation: In f(x) = a·b^x the parameter a is the y-intercept (f(0)=a). Decreasing a (but keeping it >0) lowers the graph vertically (reduces the starting value) while preserving the exponential shape, horizontal asymptote y=0, and multiplicative growth rate determined by the base.