Question

Which statements are true about the graphs of all nth degree polynomials? Choose all that apply.


1) It must go up and down a total of n times.

2) It goes up and down at most a total of n times.

3) The number of x-intercepts is n.

4) The number of x-intercepts is at most n.

5) The end of the graph must go up either to the left or the right.

6) The end behavior depends on the number of terms of the polynomial.

Answer 1

We are given

nth degree polynomial

so, we will verify each options

option-1:

this is FALSE

Because for $y=x^3$

It goes up only once

while $y=x^4$

goes up and down twice

option-2:

Since, the degree of polynomial is n

so, the maximum number of times it can go up and down as n times

so, this is TRUE

option-3:

this is FALSE

For example:

$x^5=0$

there is only one x-intercept

while degree is 5

option-4:

since, the degree of polynomial =n

so, the maximum number of x-intercepts =n

so, this is TRUE

option-5:

this is FALSE

For example:

$f(x)=x^2$

both ends go up

option-6:

this is FALSE

because end behavior of any polynomial always depend on degree and leading coefficients

Answer 2

Answer:

2) It goes up and down at most a total of n times.

4) The number of x-intercepts is at most n.

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Step-by-step explanation: