Download Algebra: Chapter 4 Review

Algebra
Chapter 4 Review
Name ______________________________
Hour _________________
1. Explain how you know the data in the table represents a function. Describe the trend in the data.
If you were to graph the data, how many points would lie in Quadrant IV?
x 1
2
3 4 5
y -7 -2 3 8 13
2. What is the range of the function in the graph?
y
70
60
50
40
30
20
10
0
5.
1
2
3
4
5
6
7 x
5
3
2
, 3) or ( , 20), is on the graph of 2x - y = 3?
2
2
3
3.
Which point, (
4.
Sketch the graphs of x = –3 and y = -1. Find the point at which the two graphs intersect.
Then graph the function using any method.
y=
3
x–1
4
1
6.
Graph the functions.
y = 4x
y=
2
x-3
3
7. Video Games The number of hours people in the United States spent playing video games each year from
1998 to 2001 can be modeled by the function f (x) = 11.9x + 46.4 where x is the number of years since 1998.
a. Graph the function and identify its domain and range.
Domain_________________
Range_______________
b. Find the value of f (x) when x = 2 Explain what the solution means in this situation.
c. Find the value of x so that f (x) = 60. Explain what the solution means in this situation.
8.
Identify the domain and range of the relation
(1,3), (2,6), (1,3), (2, 6), (3, 9), (4, 12), (5, 15)
Find the value of x or y so that the line passing through the two points has the given slope.
9. a. (x, –7), (1, 2); m =3
b. (8, 1), (1, y); m = –1
10.
Identify the x- and y-intercepts of the
line below.
11. Graph the linear equation 3x + 6y = 18
using the x- and y-intercepts.
y
10
x
–10
2
–10
12.
Mia has a jar full of dimes and quarters. She has a total of $16.00. The possible numbers of
dimes x and quarters y that Mia has can be modeled by the equation 0.10x + 0.25y = 16.
.
a. What is the x-intercept of the graph of this equation and what does it mean in the situation?
b. What is the y-intercept of the graph of this equation and what does it mean in the situation?
13. Determine the slope of the line segment below.
A__________ B___________C__________
A
B
C
14.
Find the slope of the line passing through the points
a. (–1, 1) and (4, –5).
b. (2, 6) and (-4, 10)
15.
Explain the difference between a horizontal line and a vertical line in terms of slope.
16.
Which graph below would match the situation described?
A car travelling at 23 mi/h accelerates to 45 mi/h in 5 seconds. It maintains that speed for the next 5 seconds, and then slows to a stop
during the next 5 seconds.
17.
Find the slope and y-intercept of the line with the equation
a. -9x + 3y = 54
b. 8x – 2y = -20
18. Tell whether the two equations are parallel lines.
a. y = 8x –3, 8x + y = 3
b. 2x + y = 5, –6 + 2x = y
3
19.
Write the equations in slope intercept form, then graph the equations.
a. y – 2 = -
2
(x + 6)
3
b. 3x – y – 2 = 0
20. Determine if the line -7x + 6y = 3 is parallel to the line y =
7
x+ 1.
6
21.
The cost to install and use a premium satellite-television service in a particular city is shown in the
graph. Find the slope and y-intercept of a line joining the points on the graph and explain what the slope and yintercept represents.
_________________________________
__________________________________
__________________________________
__________________________________
22.
Line A passes through the points (2, 5) and (3, 7),
Line B passes through (0, –2) and (–1, –4), and Line C passes through (–3, 5) and (–4, 7)
a. Find the slope of each line.
b. Which lines intersect each other? Which lines do not intersect each other? Explain.
23. Match the function with the description of its graph in relation to the
graph of f (x) = x.
g(x) = 4x __________
A. graph of f shifted up 4 units
g(x) = x + 4
__________
B. graph of f shifted down 4 units C. graph of f stretched by factor of 4
23. a. What is the value of the function when x = 5?
f(x) = 4x + 9
g(x) = x – 4 ___________
B. Find the value of x so that f(x) = 13.
1
f ( x)   x
4
4
5