Question

Hi I really need help on how to solve this step by step as I am very confused

Answer 1

Step-by-step 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

`\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}`

Also

`\begin{gathered} g(x)=2x-1 \\ the\text{ x-intercept is \lparen}(1)/(2),0\text{\rparen} \\ the\text{ y-intercept is \lparen0,-1\rparen} \\ This\text{ is the green graph} \end{gathered}`

then for

`\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}`

Finally for

`\begin{gathered} (g\text{ o f\rparen\lparen x\rparen=2x+2-1=2x+1} \\ the\text{ x-intercept is \lparen}(-1)/(2)\text{,0\rparen} \\ the\text{ y-intercept is \lparen0,1\rparen} \\ This\text{ is the yellow graph} \\ \end{gathered}`

With the information above, we can now match the functions