MATH SOLVE

3 months ago

Q:
# On a piece of paper graph f(x)=4^x. Then determine which answer matches the graph you drew

Accepted Solution

A:

ANSWER

See graph.

EXPLANATION

The given function is

[tex]f(x) = {4}^{x} .[/tex]

This is an exponential function of the form,

[tex]f(x) =a {b}^{kx} [/tex]

Since,

[tex]k > \: 0[/tex]

the function is an exponential growth function.

Let us look for some few points on this curve.

When

[tex]x = 0[/tex]

[tex]f(0) = {4}^{0} .[/tex]

[tex]f(0) = 1[/tex]

Hence the point

[tex](0,1)[/tex]

lies on this curve and it is the y-intercept.

When

[tex]x = 1[/tex]

[tex]f(1) = {4}^{1} [/tex]

[tex]f(1) =4[/tex]

The point,

[tex](1,4)[/tex]

also lies on this curve. So the graph of this curve must go through this point.

Now as x-values approaches negative infinity the function approaches zero.

We can use this information to obtain the graph in the attachment.

See graph.

EXPLANATION

The given function is

[tex]f(x) = {4}^{x} .[/tex]

This is an exponential function of the form,

[tex]f(x) =a {b}^{kx} [/tex]

Since,

[tex]k > \: 0[/tex]

the function is an exponential growth function.

Let us look for some few points on this curve.

When

[tex]x = 0[/tex]

[tex]f(0) = {4}^{0} .[/tex]

[tex]f(0) = 1[/tex]

Hence the point

[tex](0,1)[/tex]

lies on this curve and it is the y-intercept.

When

[tex]x = 1[/tex]

[tex]f(1) = {4}^{1} [/tex]

[tex]f(1) =4[/tex]

The point,

[tex](1,4)[/tex]

also lies on this curve. So the graph of this curve must go through this point.

Now as x-values approaches negative infinity the function approaches zero.

We can use this information to obtain the graph in the attachment.