Answer:
The new equation would be [tex]h(x) = 2x - 12[/tex]
Step-by-step explanation:
Shifting a function f(x) a units to the right is doing the following operation:
[tex]f(x) = f(x-a)[/tex]
Shifting a function f(x) a units down is doing the following operation:
[tex]f(x) = f(x) - a[/tex]
In this question:
[tex]g(x) = 2x[/tex]
Shifting 5 units to the right:
[tex]g(x-5) = 2(x-5) = 2x - 10[/tex]
Shifting 2 units down:
[tex]g(x-5) - 2 = 2x - 10 - 2 = 2x - 12[/tex]
The new equation would be [tex]h(x) = 2x - 12[/tex]
