Final review for math 114

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Math 114
Final Review
Warning: The exam will not be exactly like this. Study everything! Spring 2017
Seshu Rao
Show All Work On Exam. Specifically, show work below question.
1. Given y2 x = 4, determine if y is a function of x. (Please justify.)
2. Given the relation {(â??1,4),(â??3,5),(4,5)}, is x a function of y? (Please justify.)
3. Given the graph below, find the domain and range of the relation. Express in interval
notation. Is the relation a function? Please explain.
4. Given f(x) = â??x2 â?? 2x â?? 1, find:
(5)
(a) f(â??1)
(5)
(b) f(a2)
5. Find the domain of
and express in interval notation.
6. Given the graph of f below, answer the following questions.(Assume the graph
continues beyond the grid.)
(3)
(3)
(4)
(a) Find f(0).
(b) Find the values of x where f(x) = 4.
(c) Find the net change from x = â??2 to x = 0.
7. Simplify (â??â??,3] â?© (â??1,â??). Please graph on number line.
8. A hotel charges $90 each night for the first three nights and $70 for each
additionalnightâ??s stay. The total cost T is a function of the number of nights x that a guest
stays. Express T as a piecewise defined function.
9. A jar contains quarters and dimes totaling $3.00. If there are twice as many quarters as
there are dimes, how many of each type are there? Please label your unknowns, set up
equation, solve and check to receive full credit.
10. State the property of real numbers used in x (y z) = (x y) z. Be specific.
11. A ball is thrown vertically in the air and its height after t seconds is given by the function
below. h(t) = â??16t2 80. Find the average speed of the ball between t = 1 and t = 2
seconds.
12. Find the equation of the line containing the points (â??2,â??7) and (â??3,â??3). Express in y = mx
b form.
13. Sketch the graph of 6x â?? 4y = â??12. Please label the ordered pairs of the x and y
interceptsonthegraph.
14. A weather balloon is filled with hydrogen at the rate of 0.75 cubic feet per seconds. After4
seconds the balloon contains 12 cubic feet of hydrogen. Find a linear function that
models the volume, V of hydrogen in the ballon at any time t.
15. Find the intersection point of the the two lines below algebraically.
5x 2.
and y =
16. Given the graph below, find the intersection point graphically and algebraically.
17. Dietmar is in the process of choosing a cell phone and a cell phone plan. The first plan
charges 10 cents per minute plus a monthly fee of $25, and the second plan offers
unlimited minutes for a monthly fee of $60.
(a) Find a linear function f that models the monthly cost f(x) (in dollars) of the first plan
in terms of the number x of minutes used.
(b) Find a linear function g that models the monthly cost g(x) (in dollars) of the second
plan in terms of the number x of mintes used
(c) Determine the number of minutes for which the two plans have the same
monthlycost.
18. Given the graph of the function below, find the average rate of change between x = â??2
and x = 0
19. Classify 2×2 3x â?? 7 = 0 as either having no solution, one solution, or two solutions.
Furthermore classify the solutions as either rational, irrational, or not real. Do not solve!
(D = b2 â?? 4ac)
20. Liam is riding a train that is traveling at a constant speed of 30m/s. Liam is inside
thetrain walking in the direction the train is moving. Liamâ??s speed relative to the train at
time t is
. Find a function V that gives Liamâ??s speed relative to the ground.
2
21. Given f(x) = â??x â?? 2x 4, answer the following questions.
(a) Express in standard form by completing the square. Do not use short-cut formula.
(b) Find the vertex, y intercept, and x intercepts if they exist.
(c) Using symmetry, find an additional point and sketch the graph below. Please
labelall points found above to receive full credit.
22. A model rocket shot straight upward has its height given by h(t) = â??4.9t2 ?. Where h
is in meters and t is in seconds.
(a) When does the rocket reach a maximum height? (Round to nearest 0.1)
(b) What is the maximum height? (Round to nearest 0.1)
(c) When does the rocket hit the ground? (Round to nearest 0.1)
23. Given the graph of the function f(x) below, sketch the graph of the following
transformations. Please label the transformed points on the new graphs. Please show
steps.(One square equals one unit.)
24. Solve |2 â?? 5x| â?¥ 7. Express in interval notation.
25. Factor completely 12×2 16x â?? 3
26. A bacteria colony starts with 1000 bacteria. If the bacteria double every 20 minutes.Find:
(a) Find an exponential model for the number of bacteria x time periods after infection,
where x is the 20-minute time period.
(b) Find an exponential model for the number of bacteria t hours after infection.
27. Suppose $1000 is invested into an account that pays 5.25% compounded quarterly.
Howlong will it take to grow to $1900?
28. Simplify
29. Express 2log(
) as a single logarithm with powers and radicals.
30. Solve the following equations. Check your solutions where applicable.
(a) 3(xâ??1) = 5. (Round to 4 decimal places.)
(b) logx log(x 1) = log12
31. Sketch the graph of y = â??log2(x) using the graph of the parent function y = log2 x.
Please label the points on the graph and the vertical asymptote. State the domain of the
translated graph.

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