Determine the end behavior of the graph of the function. f (x) = 9x3(4 - x)(7x +
ID: 3115841 • Letter: D
Question
Determine the end behavior of the graph of the function.
f (x) = 9x3(4 - x)(7x + 3)4
Down left and up right
Down left and down right
Up left and up right
Up left and down right
Find the zeros of the function and state the multiplicities.
f (x) = -4x7(x - 7)4(x - 8)7
0 (multiplicity 7), -7 (multiplicity 4), -8 (multiplicity 7)
7 (multiplicity 4), 8 (multiplicity 7)
0 (multiplicity 7), 7 (multiplicity 4), 8 (multiplicity 7)
-7 (multiplicity 4), -8 (multiplicity 7)
Determine whether the intermediate value theorem guarantees that the function has a zero on the given interval.
f (x) = x3 - 5x2 - 11x + 2; [4, 5]
Yes
No
Use synthetic division to divide the polynomials.
(s4 + 4s3 - 7s2 - 16s + 21) ÷ (s - 2)
Explanation / Answer
Determine the end behavior of the graph of the function.
f (x) = 9x3(4 - x)(7x + 3)4
at x = -infinity, f(x) is negative so left down
at x = +infinity, f(x) is negative so right down
so option 2
Find the zeros of the function and state the multiplicities.
f (x) = -4x7(x - 7)4(x - 8)7
roots are 0, 7, and 8
0 (multiplicity 7), 7 (multiplicity 4), 8 (multiplicity 7)
option (c)
Determine whether the intermediate value theorem guarantees that the function has a zero on the given interval.
f (x) = x3 - 5x2 - 11x + 2; [4, 5]
f(4) = 64-80-44+2 = -58
f(5) = 125-125-55+2 = -53
so it doesn't guarantee as both the sign are negative
No is the answer
Use synthetic division to divide the polynomials.
(s4 + 4s3 - 7s2 - 16s + 21) ÷ (s - 2)
synthetic division is the method to find zeros of the equation or to find whether a number is root of the equation.
s = 2 in s4 + 4s3 - 7s2 - 16s + 21
16+32-28-32 + 21 = 9
not root
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