Question

On a piece of paper , graph f(x)=2^x then determine which answer choice matches the graph you drew.

Answer 1

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

$f(x)=2^x$

This is a exponential function of the form

$y=a(b^x)$

where

a is the initial value or the y-intercept

b is the base of the exponential function

If b>1 then is a exponential growth function

If b<1 then is a exponential decay function

In this problem

The y-intercept is equal to

For x=0

$f(x)=2^0=1$

The y-intercept is the point (0,1)

so

$a=1$

$b=2$

The value of b is greater than 1

so

Is a growth function

To plot the graph create a table with different values of x and y

For x=-1

f(x)=2^-1=0.5

point (-1,0.5)

For x=1

$f(x)=2^1=2$

point (1,2)

For x=2

$f(x)=2^2=4$

point (2,4)

For x=3

$f(x)=2^3=8$

point (3,8)

For x=4

f(x)=2^4=16

point (4,16)

Plot the y-intercept and the other points and connect them to graph the exponential function

Note that as x increases the value of y increases (exponential growth function)

The graph in the attached figure