Question

How does the graph of g(x) = −(x + 3)4 compare to the parent function of f(x) = x4?

Answer 1

Answer:

4th choice

Step-by-step explanation:

Let f(x)=x^4 be the parent function.

This is what the following means:

n(x)=(x-3)^4 : The parent function has moved right 3.

h(x)=-x^4 : The parent function has been reflected over the x-axis.

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Together (n and h):

m(x)=-(x-3)^4:  The parent function has been reflected over the x-axis and moved right 4 units.

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v(x)=(x-3)^4+5:  The parent function has been moved right 3 units and up 5 units.

So you have g(x)=-(x+3)^4.

So this consists of a reflection across x-axis and has been shifted 3 units left.

Answer 2

Answer:

g(x) is shifted 3 units to the left and reflected over the x-axis.

Step-by-step explanation:

Given the Parent function:

$x^{4}$

And the other

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

Since the g(x) function is multiplied by -(1) and added to 3 units, then the curve is translated 3 units left and reflected over the x-axis, as the graph below shows.

The negative parameter "a" reflects over the x-axis. And the independent parameters, being added to the parent one translate the curve.