Answer
graph of $f(x)=2^x-3$
Work Step by Step
Substituting $x=-2,-1,0,1,2,$ the corresponding values of $f(x)$ in the given function, $f(x)=2^x-3,$ are as follows:
\begin{align*}\require{cancel}
\text{If }x=-2:
f(-2)&=2^{-2}-3
\\&=
\dfrac{1}{2^2}-3
\\&=
\dfrac{1}{4}-3
\\&=
0.25-3
\\&=
-2.75
\\\\
\text{If }x=-1:
f(-1)&=2^{-1}-3
\\&=
\dfrac{1}{2^1}-3
\\&=
0.5-3
\\&=
-2.5
\\\\
\text{If }x=0:
f(0)&=2^{0}-3
\\&=
1-3
\\&=
-2
\\\\
\text{If }x=1:
f(1)&=2^{1}-3
\\&=
2-3
\\&=
-1
\\\\
\text{If }x=2:
f(1)&=2^{2}-3
\\&=
4-3
\\&=
1
.\end{align*}
Plotting the points $(-2,-2.75), (-1,-2.5), (0,-2), (1,-1), (2,1),$ gives the graph of $f(x)=2^x-3$.
