Answer:
[tex]g(x) = 5^{x} -10[/tex]
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 : [tex]f(x) = 5^{x}[/tex]
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
[tex]g(x) = 5^{x} -10[/tex]
