Will give
the graphs of f(x) = 5x and its translation, g(x), are shown on the graph.

on a coordinate plane, 2 exponential functions are shown. f (x) approaches y = 0 in quadrant 2 and increases into quadrant 1. it crosses the y-axis at (0, 1) and goes through (1, 5) and (2, 25). g (x) approaches y = negative 10 in quadrant 2 and increases into quadrant 1. it goes through (0, negative 9), (1, negative 5), (2, 15).

what is the equation of g(x)?

g(x) = 5x – 9
g(x) = 5x – 10
g(x) = 5x – 9
g(x) = 5x – 10

Step-by-step explanation:

See the attached figure which represents the problem.

At first we should know the rules of translation

1) {f(x) + a} is f(x) shifted up (a) units

2) {f(x) – a} is f(x) shifted down (a) units

3) {f(x + a)} is f(x) shifted left (a) units.

4) {f(x – a)} is f(x) shifted right (a) units.

The given function :

As shown on the attached graph the function g(x) is below f(x)

Which mean f(x) is shifted down.

by comparing two points with the same x-coordinate like (1,5) and (1,-5)

So, the difference will be = 5 - (-5) = 10

by applying the second rule and substitute with a = 10

g(x) = f(x) - 10

irrational, cannot