since g(x) is equal to $x^2+1$ , you just plug in the value of 2 for x, to get $2^2+1$ , and 2 to the power of 2 (also known as 2 squared) is equal to 4, which makes your equation $4+1$ , which equals 5.

3 0

3 years ago

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 neg

Mars2501 [29]

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. "

7 0

3 years ago

Read 2 more answers

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Zina [86]

Answer:

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6 0

2 years ago