Question

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

Answer 1

The two functions have the same output value $y=-1$ when their input value is $x=3$

Explanation:

The two functions are $f(x)=-\frac{2}{3} x+1$ and $g(x)=\frac{1}{3} x-2$

To determine the same output value for the two functions, let us substitute the values for x-coordinate(input value) in both the functions.

First, let us substitute the values in the function $f(x)=-\frac{2}{3} x+1$

For $x=0$  ⇒ $f(0)=1$

For $x=1$  ⇒ $f(1)=\frac{1}{3}$

For $x=2$  ⇒ $f(2)=-\frac{1}{3}$

For $x=3$  ⇒ $f(3)=-1$

Similarly, let us substitute the values in the function $g(x)=\frac{1}{3} x-2$

For $x=0$  ⇒ $g(0)=-2$

For $x=1$  ⇒ $g(1)=-\frac{5}{3}$

For $x=2$  ⇒ $g(2)=-\frac{4}{3}$

For $x=3$  ⇒ $g(3)=-1$

Thus, the two functions have the same output value $y=-1$ when their input value is $x=3$