Question

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

Answer 1

Answer:

The graph given can be further simplified as follows:

$g(x)=2x+2$

I have drawn and attached the graph with the answer.

Step-by-step 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

Answer:

The graph is shown below.

Step-by-step 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 | x ∈ R }

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.