Answer:
Please refer to the attached image for the graph of g(x).
Step-by-step explanation:
First of all, let us find the value of g(x).
Given that:
[tex]f(x) =2x-5[/tex] and
[tex]g(x) = f(x+1)[/tex]
To find: The graph of g(x) = ?
Solution:
[tex]f(x+1)[/tex] means we replace 'x' with 'x+1' and we get g(x).
Let us replace x with x+1 in f(x):
[tex]f(x+1) = 2(x+1)-5\\\Rightarrow f(x+1) = 2x+2-5\\\Rightarrow f(x+1) = 2x-3\\\therefore g(x) = 2x-3[/tex]
Now let [tex]y=g(x) =2x-3[/tex]
Let us put x = 0 and then y = 0 to find two points on coordinate axis to easily plot the graph of g(x).
Putting x = 0,
[tex]y=2\times0-3\\\Rightarrow y =-3[/tex]
So, one point is A(0,-3)
Now, let us put y = 0 and find out x.
[tex]0=2x-3\\\Rightarrow x=\dfrac{3}{2}[/tex]
So, second point is [tex]B(\frac{3}{2},0)[/tex].
Now, let us plot A and B then extend the line joining AB.
Please refer to the attached image for the graph of function:
g(x) = 2x - 3
