Question

which input value produces the same output value for the two functions on the graph?

(f(x) = -\frac{2}{3}x + 1)

(g(x) = \frac{1}{3}x - 2)

Explanation:

Identify the intersection point visually

Using the Graphical Intersection knowledge point

$$ \text{Intersection point on the graph} = (3, -1) $$

Set up the algebraic equation

Using the Systems of Linear Equations knowledge point

$$ f(x) = g(x) \implies -\frac{2}{3}x + 1 = \frac{1}{3}x - 2 $$

Solve for the input value x

Using the Systems of Linear Equations knowledge point

$$
LATEXBLOCK0
$$

Verify the output value

Using the Systems of Linear Equations knowledge point

$$
LATEXBLOCK1
$$

Answer:

\(x = 3\)