For the polynomial function ƒ(x) = x4 −25x2, find the zeros. then determine the multiplicity at each zero and state whether the graph displays the behavior of a touch or a cross at each intercept.

ANSWER

The zeros are

EXPLANATION

Given;

.

We can rewrite the function as

The zeros are found by equating the function to zero.

The multiplicity is 1, since it is odd the graph crosses at this intercept. which is

Or

The multiplicity is 1, since it is odd the graph crosses at this intercept. which is

Or

This last root has a multiplicity of 2.

That is

repeats two times.

Since the multiplicity is even, the graph touches the x-axis at the point .

See graph.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

yes

step-by-step explanation:

yes