Algebra 1 – Semester 1 Final Exam Review: Part 5
Name ___________________________________ Solve each of the following problems. Show All Work. DO NOT LOSE. You will staple this review to all other reviews and submit on the day of your Algebra 1 Final. Your Algebra 1 final exam is ______________________________________. Chapter 5: ____ 1. Identify each graph as being a non-linear function, linear function, or not a function. Graph A
Graph B
Graph C
y
y
3
5
2
4
y 3 2
1
3
1
2
–3
–2
–1 –1
1
3 x
2
–2
1
–2 –1
–3
a. Graph A: non-linear function Graph B: not a function Graph C: not a function b. Graph A: not a function Graph B: not a function Graph C: linear function ____
–1
2
3
4 x
–3
c. Graph A: non-linear function Graph B: linear function Graph C: linear function d. Graph A: non-linear function Graph B: linear function Graph C: not a function
2. Tell whether the set of ordered pairs a. Yes; there is no constant change in x that corresponds to a constant change in y. b. Yes; there is a constant change in x that corresponds to a constant change in y.
3. Use intercepts to graph the line described by the equation
satisfies a linear function. Explain. c. No; there is a constant change in x that corresponds to a constant change in y. d. No; there is no constant change in x that corresponds to a constant change in y. . Graph for # 3
4. Write the equation of the line with the slope
1
–2
x
1
–1 –1
1 3
and y-intercept –2, then graph. Graph for # 4
5. Thomas is a car salesman. He is paid a salary of $1600 per month plus $300 for each car that he sells. His salary can be modeled by the equation where x is the number of cars sold. Graph this equation and give its domain and range. f( x)
a.
5000
Monthly Salary ($)
Monthly Salary ($)
f( x)
c.
5000
4000
3000
2000
1000
4000
3000
2000
1000
2
4
6
x
8
2
4
Number of Cars Sold
f( x)
b.
6
8
x
Number of Cars Sold
D: {0, 1, 2, 3, ...} R: {$1600, $1900, $2200, $2500, ..}
D: {$300, $1900, $3500, $5100, ...} R: {0, 1, 2, 3, ...} f( x)
d.
5000
Monthly Salary ($)
5000
Monthly Salary ($)
____
4000
3000
2000
1000
4000
3000
2000
1000
2
4
6
x
8
2
4
Number of Cars Sold
D: {$1600, $1900, $2200, $2500, ...} R: {0, 1, 2, 3,...} 6. Determine if graph shows a linear relationship. Find the slope and write the equation.
6
8
x
Number of Cars Sold
D: {0, 1, 2, 3, ...} R: {$300, $1900, $3500, 5100, ...}
7. Tell whether the slope is positive, negative, zero, or undefined. Write the equation.
8. Find the slope of the line and write the equation. y 10
y
y
8
10
5
6
8
4
(–4, 3)4
6
3
4 2
1 –10 –8
–6
–4
–2 –2
(1, 2 –1) 4
6
8
10
–4
–1 –1
–6
–2
–8 –10
(7, –8)
–10 –8
x
–5
–4
–3
–2
1
2
3
4
5
x
–6
–4
–2 –2 –4 –6
–3
–8
–4
–10
–5
(6, 3)
2
2
2
4
6
8
10
x
9. Find the slope of the line and write the equation. y 8 6 4 2
–8
–6
–4
–2
2
4
6
8
x
(5, –3)
–2 –4 –6
(2, –5)
–8
10.
Find the x- and y-intercepts and write the equation of the line. y 10 8 6 4 2
–10 –8
–6
–4
–2 –2
2
4
6
8
10
x
–4 –6 –8 –10
11. Write the equation that describes the line in slope intercept form. Point (3, -5) is on the line and the slope = 2.
12. Write the equation that describes the line in slope intercept form. Points 3, 3 and 3,1 are on the line.
review chapter 5 Answer Section MULTIPLE CHOICE 1. ANS: D In a function, each domain value is paired with exactly one range value. Graph A is a function, but it is not linear. Graph B is a function and a line. Graph C is not a function because each domain value (2.8) pairs with infinite range values.
A B C D
Feedback Horizontal lines are functions. Curved graphs can be functions as long as any x value corresponds to only one y value. Vertical lines are not functions. Correct!
PTS: 1 DIF: Basic REF: Page 296 OBJ: 5-1.1 Identifying a Linear Function by Its Graph STA: A.5.C TOP: 5-1 Identifying Linear Functions
NAT: 12.5.1.e
2. ANS: B In a linear function, a constant change in x means a constant change in y. x y 1 1 +2 3 5 +4 +2 5 9 +4 constant change in y +2 7 13 +4
A B C D
Feedback If a constant change in x corresponds to a constant change in y, then the function is linear. Correct! Check to see if there is a constant change in the x-values and the y-values. This is a linear function if a constant change in x corresponds to a constant change in y.
PTS: OBJ: NAT: KEY:
1 DIF: Basic REF: Page 297 5-1.2 Identifying a Linear Function by Using Ordered Pairs 12.5.1.e STA: A.5.C TOP: 5-1 Identifying Linear Functions function | linear
3. ANS: A Choose several values for x and make a table. x 0 = 1600
1 2 3
= 1900 = 2200 = 2500
Graph the ordered pairs. The number of cars x is the independent variable, and the salary variable. The number of cars sold must be a whole number, so the domain is $1900, $2200, $2500, ...}.
A B C D
is the dependent
and the range is {$1600,
Feedback Correct! The domain is the number of cars sold. The range is the monthly salary. The monthly salary is the y-intercept. The income per car is the slope. The domain is the number of cars sold. The range is the monthly salary. The income per car is the slope.
PTS: 1 NAT: 12.5.1.g
DIF: Average STA: A.5.C
REF: Page 299 OBJ: 5-1.4 Application TOP: 5-1 Identifying Linear Functions
SHORT ANSWER 4. ANS: x-intercept: 2, y-intercept: 3 y 10 8 6 4 2 –10 –8
–6
–4
–2 –2
2
4
6
8
x
–4 –6 –8 –10
To find the x-intercept, let y = 0 and solve for x; to find the y-intercept, let x = 0 and solve for y. Then, plot the intercepts and draw a line connecting them.
PTS: OBJ: STA: KEY: 5. ANS:
1 DIF: Average REF: Page 305 5-2.3 Graphing Linear Equations by Using Intercepts NAT: 12.5.1.e A.6.E TOP: 5-2 Using Intercepts linear equation | graphing | x-intercept | y-intercept | intercepts
y 5 4 3 2 1 –5
–4
–3
–2
–1 –1
1
2
3
5 x
4
–2 –3 –4 –5
Plot the y-intercept –2 on the graph at (0, –2). The slope is 13 , so from the y-intercept, rise 1 units and run 3 units. Plot another point. Connect the points to graph the line. y 5 4 3 2 1 –5
–4
–3
–2
–1 –1
y-intercept
–2
1
2
run
3
4
5
x
rise
–3 –4 –5
PTS: 1 DIF: Basic REF: Page 334 OBJ: 5-6.1 Graphing by Using Slope and y-intercept STA: A.6.D TOP: 5-6 Slope-Intercept Form
NAT: 12.5.3.d
6. ANS: 6 7
Use the slope formula. Substitute = 76
for
and
for
.
Simplify.
PTS: 1 DIF: Basic REF: Page 321 OBJ: 5-4.2 Finding Slope from Graphs and Tables STA: A.6.A TOP: 5-4 The Slope Formula
NAT: 12.5.2.b
7. ANS: undefined A line has positive slope if it rises from left to right. A line has negative slope if it falls from left to right. A line has zero slope if it is a horizontal line. A line has undefined slope if it is a vertical line.
PTS: 1 NAT: 12.5.2.b
DIF: Average STA: A.6.B
REF: Page 312 OBJ: 5-3.5 Describing Slope TOP: 5-3 Rate of Change and Slope
8. ANS: 0 . The slope is 0.
PTS: 1 DIF: Basic REF: Page 312 OBJ: 5-3.4 Finding Slopes of Horizontal and Vertical Lines STA: A.6.A TOP: 5-3 Rate of Change and Slope
NAT: 12.5.2.b
9. ANS: 2 3
To find the slope, use the coordinates of two points on the line. Starting at one point, count the units down (negative units) or up (positive units) and to the right (positive units) or to the left (negative units) to arrive at the other point. The units up or down are the rise. The units to the right or to the left are the run. Write a fraction with the rise in the numerator and the run in the denominator. Simplify the fraction.
PTS: 1 NAT: 12.5.2.b KEY: line | slope
DIF: Basic STA: A.6.A
REF: Page 311 OBJ: 5-3.3 Finding Slope TOP: 5-3 Rate of Change and Slope
10. ANS: x-intercept: 10, y-intercept: 5 The graph intersects the x-axis at (10, 0). The x-intercept is 10. The graph intersects the y-axis at (0, 5). The y-intercept is 5.
PTS: 1 DIF: Basic REF: Page 303 OBJ: 5-2.1 Finding Intercepts NAT: 12.5.1.e STA: A.6.E TOP: 5-2 Using Intercepts KEY: linear equation | x-intercept | y-intercept | intercepts
