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this questions are mostly functions and graph nd its precalculus pls anybody can help in need for urgent answer

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MAT1375

Fall 2020

Test 1

Write clearly and show all work to get full credit. Submit it as a pdf file on

Blackboard.

Question 1 (10 points). Solve the inequalities. Write your answers in interval

notation.

a) (5 points) |4𝑥 + 9| ≥ 7

b) (5 points) |3𝑥 − 7| < 2
Question 2 (10 points). Graph the polynomial 𝑓(𝑥) = 𝑥 3 − 3𝑥 2 − 25𝑥 − 21. Find
all zeros, and local extrema from the graph. Round your answers to the nearest
hundredths.
Question 3 (10 points). Let 𝑓(𝑥) = 2𝑥 2 − 5𝑥 − 4. Simplify the difference quotient
𝑓(𝑥+ℎ)−𝑓(𝑥)
ℎ
as much as possible, ℎ ≠ 0. Check by substituting 𝑥 = −1 and
ℎ = 3 in the above formula and in your answer, and comment on the results.
Question 4 (10 points). Let 𝑓(𝑥) = 𝑥 2 − 2𝑥 − 63,
𝑔(𝑥) = 7𝑥 − 2, and
ℎ(𝑥) = √3 − 2𝑥.
a) (5 points) Find the difference (ℎ − 𝑓)(𝑥) and state its domain.
𝑔
b) (5 points) Find the quotient ( ) (𝑥) and state its domain.
𝑓
Question 5 (10 points). Let 𝑓(𝑥) = 3𝑥 2 − 2𝑥 + 1 and 𝑔(𝑥) = 4𝑥 − 3. Find the
composition
a) (5 points) (𝑓°𝑔)(𝑥);
b) (5 points) (𝑔°𝑓)(𝑥).
MAT1375
Fall 2020
Question 6 (10 points). Find the inverse of the function:
a) (5 points) 𝑓(𝑥) =
b) (5 points) 𝑓(𝑥) =
3𝑥−7
;
2−5𝑥
√𝑥 2 −
9.
Question 7) (15 points). Determine if the function is even, odd, or neither.
a) 𝑓(𝑥) = 5𝑥 2 − 3𝑥 + 2;
b) 𝑔(𝑥) = 7𝑥 7 − 3𝑥 3 − 𝑥;
c)
ℎ(𝑥 ) =
5𝑥 4 +3
𝑥2
.
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Tags:
inequalities
polynomial
precalculus
inverse functions
difference quotient
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