Question

Question in picture provided The first drop down options are LeftRightUp Down (Couldn’t show both at once)

Answer 1

Given:

f(x)=3x+1

It is given that the graph of the function g(x). we need to find the function g(x).

Consider, g(x) = f(x)-2, now substitute x=0 into the function g(x) as follows:

`\begin{gathered} g(x)=f(x)-2 \\ =3x+1-2 \\ =3x-1 \\ g(0)=3(0)-1 \\ g(0)=-1 \end{gathered}`

Therefore, the vertiex (0,-1) not shown in the givien grph.

Now, consider g(x)= f(x-2), now substitute x=0 into the function g(x) as follows:

`\begin{gathered} g(x)=f(x-2) \\ =3(x-2)+1 \\ =3x-6+1 \\ =3x-5 \\ g(0)=-5 \end{gathered}`

Therefore, the vertiex is (0,-5). Now substitute x=3 in above function as,

`\begin{gathered} g(x)=3x-5 \\ g(3)=9-5 \\ g(3)=4 \end{gathered}`

Therefore, the vertiex is (3,4). Hence, the function g(x) =f(x-2) is satisfying the given graph

Hence, the required answer is g(x)=f(x-2). The graph g(x) is translated 2 unit to the down.