Question 202·Medium·Algebra

Compute the slope, then use $y=mx+b$ to find the $y$-intercept.

The graph is of $y=3f(x)-6$. Once you know $y$ in terms of $x$, set $3f(x)-6$ equal to that expression and isolate $f(x)$.

In Desmos, define the points from the graph, for example:

• A=(-1,-6)
• B=(3,6)

Type:

• m=(y(B)-y(A))/(x(B)-x(A))
• g(x)=m(x-x(A))+y(A)

This gives the equation of the graphed line as a function $g(x)$.

Since $g(x)$ equals $y$ and the graph represents $y=3f(x)-6$, type:

• f(x)=(g(x)+6)/3

Simplify the resulting expression for $f(x)$ and match it to one of the answer choices.

From the graph, the line passes through the points $(-1,-6)$ and $(3,6)$.

Slope:

Using $(3,6)$ in $y=mx+b$:

So the graphed line is $y=3x-3$.

Because the graph shows $y=3f(x)-6$, set the expressions for $y$ equal:

Add $6$ to both sides and then divide by $3$:

Therefore, the correct choice is $f(x)=x+1$.