Explanation
The given graph is a combination of 4 different functions
To match the functions, we will have to get the x and y-intercepts of all the functions
Given that
[tex]\begin{gathered} f(x)=x+1 \\ the\text{ x-intercept is \lparen-1,0\rparen} \\ the\text{ y-intercept is \lparen0,1\rparen} \\ \\ This\text{ is the red graph} \end{gathered}[/tex]
Also
[tex]\begin{gathered} g(x)=2x-1 \\ the\text{ x-intercept is \lparen}\frac{1}{2},0\text{\rparen} \\ the\text{ y-intercept is \lparen0,-1\rparen} \\ This\text{ is the green graph} \end{gathered}[/tex]
then for
[tex]\begin{gathered} (f\text{ o g})(x)=2x-1+1=2x \\ the\text{ x intercept is \lparen0,0\rparen} \\ the\text{ y intecept is \lparen0,0\rparen} \\ This\text{ is the blue graph} \end{gathered}[/tex]
Finally for
[tex]\begin{gathered} (g\text{ o f\rparen\lparen x\rparen=2x+2-1=2x+1} \\ the\text{ x-intercept is \lparen}\frac{-1}{2}\text{,0\rparen} \\ the\text{ y-intercept is \lparen0,1\rparen} \\ This\text{ is the yellow graph} \\ \end{gathered}[/tex]
With the information above, we can now match the functions
