Let f(x) = 5x – 26 and g(x) = 6x.
Part 1 [4 points] What is (f ◦ g)(x) ?
Part 2 [2 points] Use complete sentences to describe the method you used to solve this problem.
Graph the function f(x) = –x3 + 2 (don't submit graph)
Part 1 [3 points] Use complete sentences to explain the process of graphing f(x) = –x3 + 2 .
Part 2 [3 points] What is the end behavior of f(x) = –x3 + 2 ?
The binomial x + 4 is the divisor of 3x3 + 5x2 – 26x + 8. Use complete sentences to explain how you use (either) polynomial division or synthetic division to find the quotient. Be sure to provide this quotient in your answer.
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Answers & Comments
Verified answer
(f o g)(x) = 5(6x) - 26 = 30x - 26
f(x) = -x^3 + 2
The graph of f(x) is the graph of x^3 reflected over the y-axis and shifted up 2 units.
lim f(x) = ∞
x-> ∞
lim f(x) = -∞
x-> -∞
.................3x^2 - 7x+2
.......---------------------------
x+4 | 3x^3+ 5x^2-26x+8
........3x^3+12x^2
........----------------
.................-7x^2-26x
.................-7x^2-28x
.................-------------
...........................2x+8
...........................2x+8
...........................-------
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