We must plot the following exponential function:
[tex]y=f(x)=4^x.^{}[/tex]
Replacing the values of x in the function above, we complete the table:
[tex]\begin{gathered} x=-3\rightarrow y=f(-3)=4^{-3}=\frac{1}{64}=0.015625, \\ x=-2\rightarrow y=f(-2)=4^{-2}=\frac{1}{16}=0.0625, \\ x=-1\rightarrow y=f(-1)=4^{-1}=\frac{1}{4}=0.25, \\ x=0\rightarrow y=f(0)=4^0=1, \\ x=1\rightarrow y=f(1)=4^1=4, \\ x=2\rightarrow y=f(2)=4^2=16, \\ x=3\rightarrow y=f(3)=4^3=64. \end{gathered}[/tex]
So we have the following points:
• (-3, 1/64) = (-3, 0.015625),
,
• (-2, 1/16) = (-2, 0.0625),
,
• (-1, 1/4) = (-1, 0.25),
,
• (0, 1),
,
• (1, 4),
,
• (1, 16),
,
• (1, 64).
Now, plotting each point (x, y) and joining them, we get the following graph:
One clarification: the label of the points in the graph have been rounded.
Answer
The points of the table are:
• (-3, 1/64)
,
• (-2, 1/16)
,
• (-1, 1/4)
,
• (0, 1),
,
• (1, 4),
,
• (1, 16),
,
• (1, 64).
The graph of the points and the function is:
One clarification: the label of the points in the graph have been rounded.
