Question

HELP TO ASAP Compare the graph of f(x) with the graph of k(x) = 5(x-6)².
OA. The graph of k(x) is horizontally stretched by a factor of 5 and
shifted 6 units right.
OB. The graph of k(x) is vertically stretched by a factor of 5 and shifted
6 units right.
OC. The graph of k(x) is horizontally stretched by a factor of 5 and
shifted 6 units left.

Answer 1

Parent function

• y=x²

Now look the transformations

• y=(x-6)²

x is changed and shifted 6 units right

Then

• y=5(x-6)²

Horizontally Streched with a factor of 5

Answer 2

Answer:

B)  The graph of k(x) is vertically stretched by a factor of 5 and shifted 6 units right.

Step-by-step explanation:

Translations

For a > 0

$f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}$

$f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}$

$y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a$

$y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}$

Given functions:

$f(x) = x^2$

$k(x) = 5(x - 6)^2$

Parent function:  $f(x) = x^2$

Translated 6 units right:  $f(x-6)=(x-6)^2$

Then stretched vertically by a factor of 5:   $5f(x-6)=5(x-6)^2$

$\implies 5f(x-6)=5(x-6)^2=k(x)$

Therefore, the graph of k(x) is vertically stretched by a factor of 5 and shifted 6 units right.

Learn more about translations here:

https://brainly.com/question/27845947