Question

HELP PLEASE!

Answer 1

Answer:

C. $h(x)=4(x-9)^2-17$

Step-by-step explanation:

We have been given a function $g(x)=4x^2-16$. 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.

$f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}$

$f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}$

$f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}$

$f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}$

Let us shift our given function to right by 9 units as:

$g(x)=4(x-9)^2-16$

Now, we will shift our function downwards by 1 unit.

$g(x)=4(x-9)^2-16-1$

$g(x)=4(x-9)^2-17$

Therefore, our required function would be $h(x)=4(x-9)^2-17$ and option C is the correct choice.

Answer 2

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: A. h(x) = 4(x - 9)² - 17