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

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Published on 28 Sep 2018
Department
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.
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
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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
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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?
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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.

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