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Name(on back also):

Test 1

100 points

Math 114-02

Spring 2018

Seshu Rao

Show All Work On Exam. Specifically, show work below question.

(10)

(10)

1. Given y â?? x2 = 4, determine if x is a function of y. (Please justify.)

2. Given the relation {(â??1,4),(â??3,5),(4,5),(2,5)}, is y a function of x? (Please justify.)

3. Given the graph below, find the domain and range of the relation. Express in

intervalnotation. Is the relation a function? Please explain.

(15)

Domain:

Range:

4. Sketch the graph of the following piecewise defined function. Please label three pointson

the graph.

(15)

(10)

5. Find the domain of

and express in interval notation.

â??

(10)

6. Find the range of f(x) = â?? x. Express in interval notation.

7. Given the graph of f below, answer the following questions.(Assume the graph continues

beyond the grid.)

(7)

(a) Find the values of x where f(x) = 0.

(15)

(8)

(b) Find the net change from x = â??1 to x = 1.

8. A hotel charges $95 each night for the first three nights and $50 for each additional nightâ??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.

if 0 â?¤ x â?¤ 3 if x

â?¥3

(15)

Total =100

Name(on back also):

Test 2

100 points

Math 114-02

Spring 2018

Seshu Rao

Show All Work On Exam. Specifically, show work below question.

(10) 1. Find the equation of the line containing the points (â??2,â??7) and (3,â??3). Express in y = mx

b form.

(10)

2. Find the intersection point of the the two lines below algebraically.

and

.

(10) 3. Sketch the graph of 3x â?? 4y = â??12. Please label the ordered pairs of the x and y intercepts

on the graph.

(10) 4. A weather balloon is filled with hydrogen at the rate of 0.90 cubic feet per seconds. After 3

seconds the balloon contains 15 cubic feet of hydrogen. Find a linear function that

models the volume, V of hydrogen in the ballon at any time t.

(15)

5. Given the graph below, find the intersection point graphically and algebraically.

(Assumearrows on the line.)

(15)

6. Dietmar is in the process of choosing a cell phone and a cell phone plan. The firstplan

charges 15 cents per minute plus a monthly fee of $30, and the second plan offers

unlimited minutes for a monthly fee of $90.

(5) (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.

(5) (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 minutes used

(5)

(c) Determine the number of minutes for which the two plans have the same monthly

cost.

7. A ball is thrown vertically in the air and its height in ft after t seconds is given by the

function below. h(t) = â??16t2 80t 36. Find the average speed of the ball between t = 0

and t = 3 seconds.

(15)

(15) 8. In the following application, identify your unknown quantities, assign a single

variable to your unknown, set up equation, solve your equation, check your

solution, and state your answer in a complete sentence to receive full credit.

At 9:00 AM, a freight train leaves Seattle traveling at 56 mph. At 9:15 AM, a passenger

train leaves the same station traveling in the same direction at 66 mph. How long will it

take the passenger train to catch up to the freight train?

Total: 100

Some Formulas: y â?? y1 = m(x â?? x1)

Name(on back also):

Test 3

100 points

Math 114-02

Spring 2018

Seshu Rao

Show All Work On Exam. Specifically, show work below question.

(16 pnts)

1. Factor completely. If not factorable state prime.

(8)

(a) 12×2 â?? x â?? 6

(8)

(b) x3 x2 â?? 4x â?? 4

(12 pnts) 2. Classify 2×2 â?? 3x â?? 3 = 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 pnts)

(8)

3. Given f(x) = â??2×2 2x â?? 1, answer the following questions.

(a) Express in standard form by completing the square. Do not use short-cut formula.

(5)

(b) Find the vertex and x and y intercepts.

(7) (c) Using symmetry, find an additional point and sketch the graph below. Please label all

points found above to receive full credit. (Each unit is 0.5 on both x and y axis.)

(16 pnts) 4. 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.

(8)

(a) When does the rocket reach a maximum height?

(8)

(b) What is the maximum height?

(20 pnts) 5. Solve the following and express in interval notation.

(10)

(a) |3 â?? 2x| â?¥ 7

(10)

(b) |2x â?? 5| < 2
(16)
6. Given the graph of the function f(x) below, sketch the graph of
Please label the transformed points on the new graphs. Please show all transformation
steps as we did in class.(One square equals one unit.)
(a) y = f(x)
...
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