Description

attached is the 13 algebra problems I need solved. It is over chapters 2 and 3 of algebra 110

Palomar College

Exam 2 of MATH 110 – 72586

Due by October 25th at 11:59 p.m.

Student’s Name:

Instructions: Show all your work for full credit. Indicate your answers clearly.

Problem 1. Let f (x) = 8×3 − 18×2 − 11x + 15.

(i) (5 pts) Factor f (x), given that

3

4

is a zero.

(ii) (2 pts) Solve, algebraically, f (x) = 0.

Problem 2. (5 pts) Determine whether the two functions g(x) = (x − 5)3 and h(x) =

are inverses.

√

3

x+5

2

Problem 3. (5 pts each) Solve, algebraically, each of the following two inequalities.

3−t

≥1

(i) (20 − x − x2 )(x + 2) ≤ 0

(ii)

5+t

Problem 4. (2 pts) Given P (x) = −3×5 + 2×4 + 6×2 − x + 4, use the Remainder Theorem to

determine the remainder when P (x) is divided by x − 2.

Z Note that you are not allowed to use another approach to solve this problem.

3

Problem 5.

(a) (1 pt) Graph v(x) = |x| − 3; x ≤ 0.

(b) (1 pt) Is v a one-to-one function? Justify your answer.

(c) (1 pt) What is the domain of v?

(d) (1 pt) What is the range of v?

(e) (2 pts) Find an equation for v −1 , the inverse of v.

(f ) (1 pt) What is the domain of v −1 ?

(g) (1 pt) What is the range of v −1 ?

(h) (1 pt) Graph the function v −1 .

4

Problem 6. (3 pts) Use long division to divide

6×4 + 3×3 − 7×2 + 6x − 5

.

−3 + x + 2×2

Problem 7. (4 pts each) The population in California P (t) (in millions) can be approximated

by the logistic growth function

P (t) =

95.2

1 + 1.8e−0.018t

where t is the number of years since the year 2000.

(i) Determine the population in the year 2000.

(ii) What is the limiting value of the population of California (i.e., as t −→ +∞) under this

model?

5

Problem 8. (5 pts each) Find the solution set of each of the following six equations.

(i) x2 e2x + 2xe2x = 8e2x

(ii) e2x − 6ex − 16 = 0

(iii) ln x + ln(x − 3) = ln(5x − 7)

6

(iv) log4 x − log4 (x − 1) =

(v) 41−x = 32x+5

1

(vi) 2x ln

−x=0

x

1

2

7

Problem 9. (5 pts each) Find the domain of the each of the following two functions.

t−1

(a) f (t) = π + log8 √

8−t

(b) g(x) = ln(x2 − x)

8

Problem 10. (5 pts) Find the domain, x-intercept, and vertical asymptote of the logarithmic

function f (x) = − log 1 (x + 2) and sketch its graph.

6

Problem 11. (2 pts) Find the integer that is represented by the following logarithmic expression.

log2 48 − log2 6

Problem 12. (4 pts) Condense the expression to the logarithm of a single quantity.

i

1h

log7 t + 3 log7 (1 − t) − log7 (7 + t)

4

9

Problem 13.

(a) (2 pts) Use transformations of the graph of y = ex to graph the function k(x) = −ex +4.

(b) (1 pt each) What are the domain and the range of k?

(c) (1 pt) Write an equation of the horizontal asymptote of k.

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