Download Review Chapter 3

Intermediate Algebra
Fall 2012
Study Guide for Exam 3
Exam 3 is scheduled for Thursday, October 11th and will cover chapter 3.
You may use a 3"x5" note card (both sides) and a scientific calculator. You are expected to know (or have written on your
note card) any formulas you may need. Think about any formulas you needed for homework. For example: slope formula,
point-slope formula, etc...
For Exam 3 you will need to be able to:
1. Plot and label ordered pairs, determine if a point is on a line, and read the inputs and outputs of graphs. 3.1
2. Determine whether an ordered pair is a solution to the equation, and complete x and y tables. 3.1
3. Graph linear and nonlinear equations by plotting points. Plot at least 3 points for the graph. 3.1
4. Interpret graphs. Decide which graph illustrates the story. 3.1
5. In a relation (or function), the set of values for the independent variable is called the domain. The set of values for the
Ways a point can be thought of:
dependent variable is called the range. 3.2
(x, y)
(domain, range)
(input, output)
6. Decide which relations are functions. For functions, each element of the domain can only have ONE element of the
range, but it is ok for two different elements of the domain to have the same element of the range. 3.2
Function
Function
Not a Function
7. Use the vertical line test to determine whether a graph represents a function. 3.2
8. Understand function notation. 3.2
9. Graph horizontal lines, vertical lines, and lines through the origin. 3.3
*The equation y=constant is a horizontal line
*The equation x=constant is a vertical line *The equation y  mx or ax  by  0 goes through the origin
10. Graph an equation using intercepts. Must also plot a 3rd point used as a ‘check point’. 3.3
*For x-intercept: set y=0, solve for x; (x,0)
*For y-intercept: set x=0, solve for y; (0,y)
11. Given two points, find the slope of the line passing through those two points, or state that the slope is undefined. 3.4
m
*Given
rise
run
( x1 , y1 ) and ( x2 , y2 ) , use formula to find slope, m 
y2  y1
x2  x1
12. Given the graph of a line, find the slope of the line or state that the slope is undefined. 3.4
m
up
down

right
left
m
Positive slope
up down

left right
Negative slope
Zero slope
Undefined slope
13. Graph the line with the given slope and going through the given point. Plot at least 3 points. 3.4
14. Given an equation, determine the slope and y–intercept of the line represented by that equation. 3.4
y  mx  b , where m  slope, and b  y - intercept (0, b)
15. Find an equation of the line using the slope and y–intercept from a graph. 3.4
16. When discussing real-life situations or when creating mathematical models, it is often useful to discuss slope as a
rate of change. 3.4
17. Use the slope-intercept form to construct models from graphs. 3.4
18. Write the equation of the line given a point on the line ( x1 , y1 ) and the slope of the line m . 3.5
* To write an equation given a point and a slope:
Given ( x1 , y1 ) and m use
y  y1  m( x  x1 ) , then solve for y to get into y  mx  b form.
19. Write the equation of the line given two points on a line ( x1 , y1 ) and ( x2 , y2 ) . 3.5
* To write an equation given 2 points:
1.Given ( x1 , y1 ) and ( x2 , y2 ) use m
2.Then use

y2  y1
x2  x1
to calculate m ,
y  y1  m( x  x1 ) , then solve for y to get into y  mx  b form.
20. Recognize parallel and perpendicular lines. 3.5
(same slope)
(negative reciprocal slopes)
21. Use the point-slope form to construct models from graphs. 3.5
22. Find the sum, difference, product, and quotient of functions. 3.6
23. Graph the sum of functions. 3.6
sum of functions : ( f  g )( x)  f ( x)  g ( x)
difference of functions : ( f  g )( x)  f ( x)  g ( x)
product of functions : ( f  g )( x)  f ( x)  g ( x)
f
f ( x)
quotient of functions :  ( x) 
, g ( x)  0
g ( x)
g
24. Graph linear inequalities. Use a test point to determine the shaded region (the solution). 3.7
*If
*If
y
y
y  , shade above the line.
or y  , shade below the line.
or
* For
 or 
use
and open dots
* For

use
and closed dots
or

Intermediate Algebra
Chapter 3 Exam Review
1. Determine which equation represents the graph.
Name _________________________
2. Determine whether the following relations represent a function.
a.
b.
3. Determine if the following graphs represent a function. It does represent a function, then state the
domain a range.
a.
b.
c.
4. Let g (t )  2t 3  3t 2  6
a. Find g (1)
d.
b. Find g (h)
5. If a ball is dropped from the top of a 196-foot building, its height above the ground, h, at
any time, t, can be found by the function h(t )  16t 2  196 , 0  t  3.5 . Find the height of
the ball at
a. 1 second
b. 3 seconds
6. Match each scenario to the corresponding graph.
a. A dude walked for 5
b. A dude went for a
minutes to warm up,
jogged for 20 minutes,
and then walked for 5
minutes to cool down.
i.
c. A dude took a 30-
leisurely bike ride at a
constant speed for 30
minutes.
ii.
d. A dude walked through
minute walk through his
neighborhood. He
stopped very briefly on
7 occasions to pick up
trash.
iii.
his neighborhood and
stopped 3 times to chat
with his neighbors. He
was gone from his house
a total of 30 minutes.
iv.
7. The following graph describes the number of y minutes you get from x dollars.
a. Does 30 minutes cost $6?
b. Does $10 give you 40 minutes?
Complete the following x-y table.
x
8. 4 x  3 y  6
1
9. Determine if ( ,3) is a solution to the
3
equation 3x  y  4 .
y
0
0
-2
10. Find the x- and y-intercepts of y 
x-intercept = (
,
)
11. Find the x- and y-intercepts of y 
x-intercept = (
,
2
x  4.
3
y-intercept = (
,
)
y-intercept = (
,
)
y-intercept = (
,
)
3
x.
5
)
12. Find the x- and y-intercepts of 4 x  6 y  24 .
x-intercept = ( , )
13. Say the weekly profit, P, of a widget store can be approximated by the formula P(n)  9n  25 ,
where n is the number of widgets sold.
a. If the store sold 50 widgets would it make a weekly profit of $475?
b. If the store sold 35 widgets, how much weekly profit would the store make?
c. If the store made a weekly profit of $250, how many widgets did the store sale?
y
14. Graph and label 2 points
4
m   , passing through  6,9 
5
x
y
15. Graph and label 2 points
m  undefined , passing through (5, 4)
x
y
16. Graph and label 2 points.
4 x  3 y  12
x
y
17. Graph and label 2 points.
5
y   x 1
6
x
y
18. Graph
x  4
x
y
19. Graph
y7  2
x
20. Write the equation of the line.
21. Write the equation of the line.
22. Write the equation of the line.
23. Write the equation of the line.
Formulas:
Slope-intercept
y  mx  b
Point-slope
Slope
y  y1  m( x  x1 )
24. Find the slope of the line through the points
(2, 3) and (-4, 6).
26. Find the slope of the line y=5.
m
y2  y1
x2  x1
25. Find the slope of the line 2 x  3 y  15 .
27. Find the slope of the line x=5.
For 16-19, write an equation for each line using the given information. Give your final answer in function
notation, f ( x)  mx  b .
28. Write an equation of the line with slope, m 
2
, and goes through the point (-1, 4).
3
29. Write an equation of the line that goes through the points (-2, 4) and (5, -10).
30. Write an equation of the line that goes through the point (-15, -10) and parallel to the line 2 x  5 y  10 .
31. Write an equation of the line that goes through the point (6, 8) and perpendicular to the line that
goes through the points (2, 4) and (6, 10).
32. Determine whether the two lines are parallel, perpendicular, or neither.
a.
b.
2x  3y  7
 3x  4 y  7
 3x  2 y  8
3
y  x7
4
c.
4 x  2 y  13
 2 x  4 y  9
33. Two points on l1 and l2 two points on are given. Determine whether is l1 parallel to l2 , l1 is
perpendicular to l2 , or neither.
a.
b.
c.
l1 : (2, 3) and (3, 2)
l1 : (3, 5) and (2, 3)
l1 : (7, 3) and (4, 6)
l2 : (4, 1) and (1, 4)
l2 : (4,  2) and (1, 2)
l2 : (5, 2) and (6, 3)
34. The following graph shows the number of Social Security beneficiaries, n, from the years 1980
projected through 2070. The function n(t), (represented by the dashed line) that can be used to
approximate this data. Let t be the number of years after 1980.
a. Determine the linear function that can be used to estimate the number of Social Security
beneficiaries, n, from the years 1980 projected through 2070.
b. Use the function determined in part a) to determine the number of Social Security beneficiaries
in the year 2020.
c. Use the function determined in part a) to estimate the year at which the number of Social
Security beneficiaries will be 60 million.
35. The number of calories burned in 1 hour of swimming, when swimming between 20 and 50 yards
per minute, is a linear function of the speed of the swimmer. A person swimming at 30 yards per
minute will burn about 489 calories in 1 hour. While swimming at 50 yards per minute a person will
burn about 525 calories in 1 hour. This information is shown in the following graph.
a. Determine a linear function that can be used to estimate the number of calories, C, burned
in 1 hour when a person swims at r yards per minute.
b. Use the function determined in part a) to determine the number of calories burned in 1 hour
when a person swims at 40 yards per minute.
c. Use the function determined in part a) to estimate the speed at which a person needs to
swim to burn 600 calories in 1 hour.
36. Let f ( x)  x 2  3x  4 and g ( x)  2 x  5
a.
b.
Find
( f  g )( x)
d.
c.
Find
( f  g )(a)
e.
f.
Find
( f  g )(1)
Find
( f  g )( x)
g.
h.
Find
( f  g )(3)
Find
( f  g )(4)
Find
( f  g )(1)
i.
Find
( f / g )(1)
Find
( f / g )(2)
37. The double line graph below compare high temperatures in Honolulu and Miami in August. From the
days listed, use the graph to answer the following questions.
a. Use the graph to find the combined temperature on
August 15th.
b. Use the graph to find the difference in temperatures
on August 16th.
y
38. Graph
5x  3 y  9
x
y
39. Graph
x  2y  0
x
40. Graph
y
4 x  3 y  12
x
y
41. Graph
 6 x  4 y  8
x
42. Graph
y
2x  5
x
y
43. Graph
y 3  4
x
44. Find the inequality that describes the shaded region.
45. Find the inequality that describes the shaded region.