Question

15 points attached file

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

f(x) equals negative StartFraction 2 Over 3 EndFraction x plus 1. g(x) equals StartFraction 1 Over 3 EndFraction x minus 2. A coordinate grid with two lines. One line labeled f(x) passes through (negative 3, 3), (0, 1), and point (3, negative 1). The second line is labeled g(x) and passes through (negative 3, negative 3), (0, negative 2), and point (3, negative 1).

x = –3
x = –1
x = 1
x = 3

Answer 1

Explanation:

x=-3

Answer 2

x = 3 renders the same output for both functions

Explanation:

From the graph, we see that at the point x = 3 both lines intersect. This means that their y value coincide for that value of x.

We check using the functions' expressions to verify that our answer is correct. Then we evaluate both functions separately at x = 3:

`f(3)= -(2)/(3) (3) + 1 = -2 + 1 = -1\\g(3) = (1)/(3) (3) -2 = 1-2 =-1`

So we conclude that effectively, the input x=3 produces equal output value (-1) for the two given functions.