Question

Make a table of values and a graph for the functionWhat is the domain?What is the range?

Answer 1

Answer and Explanation:

Given:

$f(x)=(0.2)^x-3$

Let's go ahead and chose different values of x and corresponding values of y;

When x = -2;

$\begin{gathered} f(-2)=(0.2)^{-2}-3 \\ =25-3 \\ =22 \end{gathered}$

When x = -1;

$\begin{gathered} f(-2)=(0.2)^{-1}-3 \\ =5-3 \\ =2 \end{gathered}$

When x = 0;

$\begin{gathered} f(0)=(0.2)^0-3 \\ =1-3 \\ =-2 \end{gathered}$

When x = 1;

$\begin{gathered} f(1)=(0.2)^1-3 \\ =0.2-3 \\ =-2.8 \end{gathered}$

When x = 5;

$\begin{gathered} f(5)=(0.2)^5-3 \\ =0.00032-3 \\ =-2.99 \end{gathered}$

With the above values, we can go ahead and graph the function as seen below;

The domain of a function is the set of possible input values(x-values) for which the function is defined. On a graph, it is the set of x-values from left to right.

Looking at the given graph, we can see that the domain is;

$Domain:(-\infty,\infty)$

The range of a function is the set of possible output values(y-values). It is the set of y-values from the bottom to the top of the graph.

Looking at the given graph, we can see that the range is;

$Range:(-3,\infty)$