Question

How does the graph of g(x) = −(x − 2)4 compare to the parent function of f(x) = x4?

g(x) is shifted 2 units to the right and reflected over the x-axis.
g(x) is shifted 2 units to the left and reflected over the x-axis.
g(x) is shifted 2 units to the right and 1 unit up.
g(x) is shifted 2 units to the right and 1 unit down.

Answer 1

Given:

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

$f(x)=x^4$

To find:

How does the graph of g(x) compare to the parent function of f(x)?

Solution:

The translation is defined as

$g(x)=kf(x+a)+b$                .... (1)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.

If k<0, then graph of f(x) reflected over x-axis.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

We have,

$f(x)=x^4$

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

So,

$g(x)=-f(x-2)$    ...(2)

From (i) and (ii), we get

$k=-1<0$, it means g(x) reflected over the x-axis.

$a=-2<0$, it means g(x) shifted 2 units to the right .

Therefore, the correct option is A.

Answer 2

Answer:

A. g(x) is shifted 2 units to the right and reflected over the x-axis.

Step-by-step explanation: