Question

Complete the statements about the key features of the graph of f(x) = x5 – 9x3. As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity.
Choose all of the zeroes of f(x).
–3 with multiplicity 1
3 with multiplicity 1
0 with multiplicity 1
0 with multiplicity 3
3 with multiplicity 0

Answer 1

The function is $f(x)= x^{5} -9x ^{3}$

1. let's factorize the expression $x^{5} -9x ^{3}$:

$f(x)= x^{5} -9x ^{3}= x^{3} ( x^{2} -9)=x^{3}(x-3)(x+3)$

the zeros of f(x) are the values of x which make f(x) = 0.

from the factorized form of the function, we see that the roots are:

-3, multiplicity 1
3, multiplicity 1
0, multiplicity 3

(the multiplicity of the roots is the power of each factor of f(x) )


2.  
The end behavior of f(x), whose term of largest degree is $x^{5}$, is the same as the end behavior of  $x^{3}$, which has a well known graph. Check the picture attached. 

(similarly the end behavior of an even degree polynomial, could be compared to the end behavior of $x^{2}$)

so, like the graph of $x^{3}$, the graph of $f(x)= x^{5} -9x ^{3}$ :

"As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity. "

Answer 2

Answer:

Negative, Positive///A,B,D////crosses

Step-by-step explanation:

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