urgentprecalculus final exammath

MATH 130 (Precalculus) Spring

2

020

Final Exam Monday, May 18—Wednesday, May 20

1. You are allowed to use the following resources: textbooks, notes, and lectures.

2. All other resources are prohibited. In particular, you may not discuss any aspect of the problems with

other people, and you may not use other computational resources.

3. Write your answers on a separate piece of paper, and show all your work. Answers without appropriate

work shown might not receive full credit.

4. Submit your exam via e-mail (NOT Gradescope) by 9:30PM on Wednesday, May 20.

5. In case I have any doubts that the work you submit is your own, I reserve the right to ask you to

demonstrate your knowledge in a one-on-one video interview.

By signing your name below, you affirm that you understand the instructions and that you have neither

given nor received unauthorized help on this exam.

I pledge that I have neither given nor received assistance on this exam.

Name (Print) Signature

Problem Value Points

1 6

2 6

3 6

4 6

5 6

6 8

7 6

8 6

9 6

10 6

11 6

12 8

13 6

14 6

15 6

Total 100

(1) Find the x− and y−intercepts of the line passing through the points (−3, 5) and (7,−10). For full

credit, all intercepts must be given as ordered pairs.

(2) If f(x) = 2×2 −x + 6, find f(x+h)−f(x

)

h

in simplest form. (Your answer will involve both x and h.)

(3) (3 points each) Given the parent function f(x) = 1

x

, write down the function whose graph satisfies the

given description in each case:

(a) The graph of f shifted 0.8 units up and 3 units to the right.

(b) The graph of f shifted 2 units to the left and then reflected through the x−axis.

(4) (a) (4 points) If f(x) =

√

x and g(x) = x2−x + 1, find both (f ◦g)(x) and (g◦f)(x) in simplest form.

(b) (2 points) If h(x) = ln(2x−3), find f and g such that h(x) = (f ◦g)(x) and neither f(x) nor g(x)

is equal to x.

(5) If f(x) = 4x−7

3x−5, find the inverse of f.

(6) Find all solutions in [0, 2π) of the following equation:

2 cos2 x + 5 sin x + 5 = 0

(7) Write the following expression as a sum of constant multiples of logarithms of a single variable. Assume

that all variables represent positive numbers.

log3

( √

x

y8 · 5

√

z3

)

(8) Find the solution set of the following equation:

log2(3x + 4) − log2(x− 2) = 3

(9) Verify the following trigonometric identity:

sin x

1 − sin x

= sec x tan x + tan2 x

(10) If sin θ = 7/10 and θ is in the 1st quadrant, find all six trigonometric functions of π

2

−θ.

(11) If cos θ = −5/9 and θ is in the 3rd quadrant, find tan 2θ.

(12) Find the solution set of the following equation:

e3x − 13e2x + 42ex = 0

(13) Find real numbers a and b such that the graph of y = a sin x + b has y−intercept equal to (0, 4) and

passes through the point (π

6

, 1).

(14) Find the domain of each of the following functions in interval notation:

(a)

√

6 − 7x (b) ln x

2x−16

(15) (a) Write the standard form of the following quadratic equation:

y = 3×2 − 8x− 6

(b) Write the vertex and axis of symmetry for the graph of the equation in part (a). For full credit, the

vertex must be given as an ordered pair and the axis of symmetry must be represented by an equation.

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