f(x) + n - shift the graph n units up
f(x) - n - shift the graph n units down
f(x + n) - shift the graph n units left
f(x - n) - shift the graph n units right
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g(x) = 4x² - 16
Shift 9 units right and 1 unit down. Therfore:
g(x - 9) - 1 = 4(x - 9)² - 16 - 1 = 4(x - 9)² - 17
Answer:
C. [tex]h(x)=4(x-9)^2-17[/tex]
Step-by-step explanation:
We have been given a function [tex]g(x)=4x^2-16[/tex]. We re asked to find the equation for function that is obtained from shifting our given function 9 units to the right and 1 down.
Let us recall transformation rules.
[tex]f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}[/tex]
[tex]f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}[/tex]
[tex]f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}[/tex]
[tex]f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}[/tex]
Let us shift our given function to right by 9 units as:
[tex]g(x)=4(x-9)^2-16[/tex]
Now, we will shift our function downwards by 1 unit.
[tex]g(x)=4(x-9)^2-16-1[/tex]
[tex]g(x)=4(x-9)^2-17[/tex]
Therefore, our required function would be [tex]h(x)=4(x-9)^2-17[/tex] and option C is the correct choice.
