Question

graph g(x), where f(x) = 2x - 5 and g(x) = f(x + 1).

Explanation:

Step1: Find the expression for g(x)

Given \(f(x)=2x - 5\) and \(g(x)=f(x + 1)\), substitute \(x+1\) into \(f(x)\):
\[g(x)=2(x + 1)-5=2x+2 - 5=2x-3\]

Step2: Find the y - intercept of g(x)

Set \(x = 0\) in \(g(x)\):
\[g(0)=2\times0-3=-3\]

Step3: Find the x - intercept of g(x)

Set \(g(x)=0\):
\[2x-3 = 0\Rightarrow2x=3\Rightarrow x=\frac{3}{2}=1.5\]
The line \(g(x)=2x - 3\) has a y - intercept of \(-3\) and an x - intercept of \(1.5\).

Answer:

We need to find the graph of the line \(y = 2x-3\). The line with a y - intercept of \(-3\) and an x - intercept of \(1.5\) is the correct graph for \(g(x)\). Without seeing the full set of options clearly, we know that the line should cross the y - axis at \((0,-3)\) and the x - axis at \((1.5,0)\). If we assume the standard form of graphing with grid - lines and the general layout of the options, we can identify the correct graph based on these intercepts.