Question

What happens to an exponential function as the values of $x$decreases? Will the graph ever cross the $y$-axis? Explain.

Short answer

As $x$decreases,

In exponential decay function ,the output values grow without bound.

In exponential growth function, the output values grow smaller, approaching zero .

Yes, the graph crosses the $y$-axis at $\left(0,1\right)$.

Step-by-step solution

Step 1 Definition for the exponential function.

The exponential function is a function which has $x$as an exponent.

For examples,

$2^x,e^x$.

Step 2 In exponential growth function,

as $x$decreases, the output values grow smaller, approaching zero .

In exponential decay function, as $x$decreases ,the output values grow without bound.

Yes the graph crosses the$y$-axis at$\left(0,1\right)$.