Question

Fill in the table and sketch the exponential function on a graph. y = 4^xxy-3-2-1023

Answer 1

We must plot the following exponential function:

`y=f(x)=4^x.^{}`

Replacing the values of x in the function above, we complete the table:

`\begin{gathered} x=-3\rightarrow y=f(-3)=4^(-3)=(1)/(64)=0.015625, \\ x=-2\rightarrow y=f(-2)=4^(-2)=(1)/(16)=0.0625, \\ x=-1\rightarrow y=f(-1)=4^(-1)=(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}`

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.