Question

Which is the graph of g(x) = 2x – 1 + 3?

Answer 1

The graph given can be further simplified as follows:

`g(x)=2x+2`

I have drawn and attached the graph with the answer.

Explanation:

The graph given can be further simplified as follows:

`g(x)=2x-1+3`

`g(x)=2x+2`

Slope of the graph is 2 as x has a coefficient of 2 and intercept is 2.

To graph the above substitute several values to x and calculate the corresponding g(x) values.

`g(1)=2*1+2\\g(1)=4`

So when x=1, g=4

`g(3)=2*3+2\\g(3)=8`

So when, x=3, g=8

Calculate several values in the same way and then plot the values is a Cartesian plane, x values in x axis and take g(x) values as y axis.

Then you will get a few dots in a straight line, join those dots with a line and that is the graph.

I have drawn and attached the graph with the answer.

Answer 2

The graph is shown below.

Explanation:

The given function is

`g(x)=2^(x-1)+3`

It is an exponential function.

The given exponential function is defined for all real numbers. So, the domain of given function is all real numbers.

Domain = x

Domain = (-∞,∞)

We know that

`2^(x-1)>0`

Add 3 on both sides.

`2^(x-1)+3>0+3`

`g(x)>3`

Range of the function is

Range = (3,∞)

Table of values is

x y

0 3.5

1 4

2 5

Plot these point on a coordinate plane.

The graph of given function is shown below.