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UT Martin Math 140 Practice Test: Functions and Graphs - Prof. Yelena Meadows, Exams of Mathematics

A practice test for ut martin math 140 students covering topics on functions and graphs. The test includes determining quadrants of points, graphing equations, finding intercepts, identifying functions, evaluating functions, transforming functions, and analyzing function behavior. Students are required to solve problems involving determining x and y intercepts, identifying increasing, decreasing, and constant intervals, and finding relative maxima and minima.

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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UTMartin Math140
FunctionsandGraphs PracticeTest
Instructor:YelenaMeadows Page1
1. Determinewhichquadranteachpointbelongstowhenplottedintherectangularsystem.
󰇛2,7󰇜
󰇛1,9󰇜
󰇡
,2󰇢
󰇛3,2󰇜
󰇛0,5󰇜
2. Grapheachequation.

3
|1
|

1

2
3. Determinethexintercept(s),ifany;yintercept(s),ifany,ofthegraphgivenbelow(eachtick
markrepresentsoneunit).
4. Determinewhichrelation(s),ifany,arefunctions.
󰇝󰇛1,2󰇜,󰇛1,3󰇜,󰇛1,4󰇜,󰇛1,5󰇜󰇞
󰇝󰇛2,1󰇜,󰇛3,1󰇜,󰇛4,1󰇜,󰇛5,1󰇜󰇞
󰇝󰇛1,2󰇜,󰇛3,4󰇜,󰇛5,6󰇜,󰇛7,8󰇜󰇞
󰇝󰇛1,2󰇜,󰇛3,4󰇜,󰇛5,6󰇜,󰇛5,8󰇜󰇞
5. Determinewhichequationdefinesyasafunctionofx.
20
2
0
21
21
1

pf3
pf4
pf5

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Functions and Graphs Practice Test

  1. Determine which quadrant each point belongs to when plotted in the rectangular system.

  1. Graph each equation.

  1. Determine the x‐intercept(s), if any; y‐intercept(s), if any, of the graph given below (each tick

mark represents one unit).

  1. Determine which relation(s ), if any, are functions.
  1. Determine which equation defines y as a function of x.

Functions and Graphs Practice Test

  1. Evaluate each function.

ሺݔሻ ൌ െ|1 െ |ݔ൅ 3 find ݂ ሺ5ሻ

  • ݂ ሺݔሻ ൌ 2 ݔ൅ 1 find ݂ ሺ ݔെ 1ሻ

െ ݔ find ݂

൅ ݔെ 1 find ݂ ሺ3ܽ ሻ

  1. Let ݃ ሺݔሻ ൌ √ݔ write an equation of ݂ ሻݔሺ if it is obtained from ݃ ሻݔሺ via:
    • Horizontal shift 2 units left;
    • Horizontal shift 2 units right;
    • Vertical shift 2 units down;
    • Vertical shift 2 units up;
    • Vertical stretch by a factor of 2;
    • Horizontal stretch by a factor of 2.
  2. Let ݄

write an equation of ݂

if it is obtained from ݄

by:

  • Reflection about the x‐axis;
  • Reflection about the y‐axis.
  1. Use vertical line test to identify which graph represents a function.
  2. Use the graph to answer the following (each tick mark is one unit):
  • For what x‐value(x), if any,
  • Domain of ݃ ሻݔሺ
  • Range of ݃ ሻݔሺ

Functions and Graphs Practice Test

  1. Determine if each function is even, odd, or neither.
  2. Find the slope of the line passing through (‐1,3) and (3,5)
  3. Write the equation of the line whose slope is െ

and is passing through (8,1)

  1. Write the equation of the line whose x‐intercept is 3 and y‐intercept is ‐6.
  2. Rewrite 2 ݔെ ݕ൅ 7 ൌ 0 in slope‐intercept form, state the slope and y‐intercept.
  3. Find the value of y if the line through points ሺ2,3ሻ and ሺെ4, ݕሻhas slope of ‐2.
  4. Write the equation of the line passing through (4,‐5) perpendicular to the line x = 4.
  5. Write the equation of the line passing through (0,2) parallel to the line whose equation

isൌ ݕ

  1. The graph shows car value depreciation. Find a linear model for the data, find the slope and

interpret its meaning.

Non‐factual Data

[Hint: Let 200 be represented by x = 0, use a graphing utility to find the line of best fit with linear

regression.]

26

23

21

19

14

0

5

10

15

20

25

30

2000 2001 2002 2003 2004

Market Value of a Car

(in thousands)

Market value of a

car (in thousands)

Functions and Graphs Practice Test

  1. The graph of the function is given below. Graph 2 ݂ሺ ݔ൅ 2ሻ ൅ 3 in the same coordinate plane.

௫ିଵ

and ݃

. Determine domain of each of the following functions:

ሺݔሻ ൌ √ ݔ൅ 7 and ݃ ሺݔሻ ൌ √ ݔെ 1

. Determine domain of each of the following functions:

  1. Determine if the two functions are inverses of each other.

ݔെ 1 and ݃ ሺݔሻ ൌ

and ݃

  1. Find the equation for ି݂

ሻݔሺ for

f ( x )