Question

Algebra 2 honors, exponential growth Need help solving this practice homework !!!

Answer 1

ANSWER and EXPLANATION

The general form of an exponential function is:

`y=a(b)^x+c`

where b = base

Hence, the base of the given function is 3.

Since the base of the function is greater than 1, then, it is an exponential growth function.

The y-intercept of the function is the point where the function touches the y-axis. From the graph, the y-intercept of the given function is (0, -2).

The key point of the function is:

`(1,3)`

The horizontal asymptote of an exponential function is given by the line:

`y=c`

Note: c is gotten from the general form of an exponential function written above.

Comparing the given function with the general form of the function, we see that the horizontal asymptote of the function is:

`y=-3`

The domain of the function is the set of all the x values (input values) of the function (graph) while its range is the set of all the y values (output values) of the function.

Hence, the domain of the function is:

`D\colon(-\infty,\infty)`

and the range of the function is:

`R\colon(-3,\infty)`