# ECON 2002.01 Study Guide - Final Guide: Complete Graph, Graphing Calculator, Tall Lighthouse

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Published on 28 Sep 2018

School

Department

Course

Professor

MSLC – Math 1150

Final Exam Review

Disclaimer: This should NOT be used as your only guide for what to study.

1. Use the piece-wise defined function

22 if 0

() 2 4 if 3

xx

fx xx

to answer the following:

a. Compute f(0), f(3), f(-1), and f(4).

b. Plot the points you found above and sketch a complete graph of y = f(x).

2. Use your graphing calculator to graph each of the functions below over the interval

2,2

and approximate

any local extrema. Also, determine the intervals where the functions are increasing and decreasing.

Round your answers to three decimal places where appropriate.

a.

2

f x x

b.

22

11g x x x

c.

h x x

d.

11k x x x x

3. Determine the average rate of change of the functions between the given values of x.

a.

3 17h x x

from

1 to 2xx

b.

2

31

x

fx x

from

1 to x x t

c.

1

1

gx x

from

0 to x x a

4. Write the equation o the function

F x x

transformed in the following ways:

a. shifted 2 units to the left, and shifted up 3 units

b. reflected about the x-axis, then shifted down 3 units

c. shifted 1 unit to the right, and vertically stretched by a factor of 3

d. shifted 1 unit to the left, then reflected about the y-axis

5. Given

31

5 and 41

f x x g x x

find:

a.

fg

b.

gf

c.

ff

d.

gg

6. Find the inverse of each function, state the domain and range of both the original function and its inverse.

a.

21f x x

b.

31g x x

c.

1

3

kx x

d.

52

x

hx x

7. Algebraically find the maxima and minima of the functions given.

a.

3 2 5f x x x

b.

2

7

53

xx

gx

8. Find all real zeros and the multiplicity of those zeros for the given polynomials, then find their y-intercepts

and sketch the graph.

a.

2 1 1 3p x x x x

b.

3

1

413p x x x

c.

22

13p x x x

9. Find all zeros (both real and complex) of the following polynomials.

a.

53

7P x x x

b.

36P x x x

c.

5 3 2

88P x x x x

10. Factor the polynomials into linear and irreducible quadratic factors with real coefficients.

a.

432

2 2 2 3P x x x x x

b.

42

22Q x x x x

11. Factor the polynomials into linear factors with complex coefficients.

a.

432

2 2 2 3P x x x x x

b.

42

22Q x x x x

12. Find a polynomial with integer coefficients having the following properties:

a. Degree: 3 Zeros: 0, i

b. Degree: 3 Zeros: –3,

1i

13. Find all intercepts and asymptotes, then sketch the graph of each rational function.

a.

2

2

4

x

Rx xx

b.

2

2

3

6

xx

Rx xx

c.

3

2

4

21

x

Rx xx

14. Solve the following inequalities. Write your answer using interval notation.

a.

5 1 2 9 3xx

b.

2 1 1

3 2 6

xx

c.

2

3 1 0xx

d.

3

1

xx

x

e.

4 1 17x

f.

2 1 5x

15. Solve the equation.

a.

2 1 2 1

24

ww

b.

9

27 81

xx

c.

2ln( ) ln(15 34)rr

d.

4

log (2 1) 2x

e.

2

3

log 24 4xx

f.

24

x

e

g.

2

6

log 6 41 2xx

h.

21

3 3 2

xx

i.

2 1 3

4·5 3

xx

16. How much needs to be invested now in order to have $1000 in 5 years given a 4.2% interest rate that is

compounded:

a. daily?

b. continuously?

17. Determine (correct to 3 decimal places) how long it will take for $2000 to double if it’s invested in an

account that gives 6% interest compounded:

a) semiannually?

b) quarterly?

c) monthly?

d) daily?

e) continuously?

## Document Summary

Also, determine the intervals where the functions are increasing and decreasing. 22if0()24if3xxfxxx 2,2 2fxx 2211gxxx hxx 11kxxxx 317hxx 1 to 2xx 231xfxx 1 to xxt 11gxx 0 to xxa fxx 315 and 41fxxgxx fggfffgg6. Find all intercepts and asymptotes, then sketch the graph of each rational function: solve the following inequalities. The frog population in a small pond grows exponentially. The current population is 70 frogs, and the relative growth rate is 15% per year: find a function that models the population after t years, use your equation to find the projected population after 3 years. Round your answer to the nearest frog: use your equation to find the number of years required for the frog population to reach 550 frogs. Round your answer to two decimal places: in the circle pictured below, r is the radius of the circle, A is the area of the sector, and s is the length of the arc subtended by the central angle.