Question

How does the graph of g(x) = −(x + 3)4 compare to the parent function of f(x) = x4?
A . g(x) is shifted 3 units to the right and 1 unit up.
B . g(x) is shifted 3 units to the right and 1 unit down.
C . g(x) is shifted 3 units to the right and reflected over the x-axis.
D . g(x) is shifted 3 units to the left and reflected over the x-axis.

Answer 1

Answer:

c. g(x) is shifted 3 units to the right and reflected over the x axis

Answer 2

Answer:

C.g(x) is shifted 3 units to the right and reflect over the x- axis.

Step-by-step explanation:

We are given that two functions

$f(x)=x^4$

and $g(x)=-(x+3)^4$

We have to compare the graph of g(x) with the graph of f(x).

When we shift f(x) towards 3 units right on x- axis then we get

$f(x)=(x+3)^4$

Using property :f(x)=f(x+c) when graph shift c units towards right side of origin on x- axis.

Now, we reflect the graph over the x- axis

Then we get

$f(x)=-(x+3)^4$

Reflection is a rotation of 180 degrees about any axis.When we rotate 180 degrees over x- axis then,  the  sign of graph is replaced by negative sign because graph shift on negative y- axis.

$f(x)=-f(x)$

When we rotate 180 degrees over y- axis then , the sign is replaced by negative sign because the graph shift on negative x- axis.

$f(x)=f(-x)$

Hence, option C is true.

Answer : C.g(x) is shifted 3 units to the right and reflect over the x- axis.