Question

Drag the dot to the correct location on the graph. Consider the following functions.

Answer 1

We are given the following functions:

$\begin{gathered} f(x)=\frac{1}{3}x-1 \\ g(x)=2x+4 \end{gathered}$

Two find the point of interception of the two functions we must first equate both functions, like this:

$f(x)=g(x)$

replacing the values:

$\frac{1}{3}x-1=2x+4$

Now we solve for "x" first by subtracting "2x" on both sides.

$\frac{1}{3}x-2x-1=2x-2x+4$

Solving the operations:

$-\frac{5}{3}x-1=4$

Now we add "1" on both sides:

$-\frac{5}{3}x-1+1=4+1$

Solving the operations:

$-\frac{5}{3}x=5$

Now we multiply both sides by 3

$-5x=15$

Now we divide both sides by -5

$x=\frac{15}{-5}=-3$

Now we replace the value of "x" in any of the two functions. Replacing in g(x), we get:

$g(-3)=2(-3)+4$

Solving the operations:

$g(-3)=-6+4=-2$

Therefore, the function intercept at the point (x,y)=(-3,-2)