Question

Hi I would love for help for all of this please

Answer 1

Given f(x) below:

$f\mleft(x\mright)=x^4-3x^3-x^2+3x$

Part 5

If f(x) is reflected over the x-axis to get g(x), then. the transformation rule is given as:

$f(x)\to g(x)=-f(x)$

Therefore, the rule for g(x) is:

$g(x)=-x^4+3x^3+x^2-3x$

To answer the other questions, we use the graph below:

The green graph is f(x) while the green graph is g(x).

Part 6

The x-intercepts are the points where the functions intercept the x-axis.

• The number of x-intercepts in f(x) = 4

,

• The number of x-intercepts in g(x) = 4

Part 7

The y-intercepts are the points where the functions intercept the y-axis.

• The number of y-intercepts in f(x) = 1

,

• The number of y-intercepts in g(x) = 1

Part 8

The local maxima are the points where the function has a maximum value.

• The number of local maximum in f(x) = 1

,

• The number of local maximum in g(x) = 2

Part 9

The local minimums are the points where the function has a minimum value.

• The number of local minimum in f(x) = 2

,

• The number of local minimum in g(x) = 1