Algebra 2: Exam #2 Study Guide
Name:_______________________________Period:_______Score:________/100
Directions: Determine the equation of the line with the given slope passing through the given
point. A) Provide the equation of the line in point-slope form. B) Provide the equation of the
line in slope intercept form. C) Provide the equation of the line in standard form with integer
coefficients. Place your answers on the correct line below. (5 points total for each)
3
1) (2, 6), m = -3
A) Point-slope form:
2) (-9, 1), m = 4
______________ A) Point-slope form:
________________
B) Slope intercept form: ______________ B) Slope intercept form: ________________
C) Standard form:
______________ C) Standard form:
Directions:
A) Write each equation in slope-intercept form.
B) Write the x-intercept as an ordered pair.
C) Write the y-intercept as an ordered pair.
________________
(3 points total for each)
3) x - 3y = 9
4) 9x + 6y = 12
A)_______________________
A)_______________________
B)_______________________
B)_______________________
C)_______________________
C)_______________________
5) Identify the slope of the line passing through the given points. Circle your final answer.
(2 points each)
A) (-3, 2) (-7, 2)
B) (3, -8) (-1, 2)
C) (3, 5) (3, -6)
6) Determine the slope intercept form of the line that goes through the given points. Then
graph the line. (3 points each)
A) (6, -4) and (-6, 2)
B) (-3, 2) and (3,6)
The equation of the line. ______________
The equation of the line. _______________
6
6
4
4
2
2
-5
5
-5
5
-2
-2
-4
-4
-6
-6
Directions: Solve each inequality. Provide a graph for your solution on a number line and
write your answer using interval notation. (3 points each)
7) -3x -1  11
8)
2x  3
1
9
Directions: Solve this problem algebraically. Show all your work. Write an inequality to
represent the situation. Be sure to describe your variables. Provide your answer in a complete
sentence. (4 points)
9) Guido, the gardener, charges a flat fee of $50 for a gardening consultation. If you decide to
hire Guido, he charges $25 an hour for labor. Ganther, the other gardener, charges a
consultation fee of $100 but only charges $15 an hour for labor. For what lengths of time is
Guido more expensive that Ganther?
Directions: Graph the following on the coordinate planes provided. Be sure to provide the
appropriate shading when necessary. (3 points each)
10)
y
x
3
2
11) 5  3x  4  10
12) 3x - 4y > 8
6
6
6
4
4
4
2
2
2
-5
5
-5
5
-5
5
-2
-2
-2
-4
-4
-4
-6
-6
-6
Directions: Solve each absolute value inequality. Provide a graph for your solution on a
number line and write your answer using interval notation. (5 points each)
13) 2x  7  3
14) 2
3x  4
8
5
Directions: Solve each equation. Show all your work. Circle your final answer(s).
(5 points each)
15) 30  2 3  5x  16
16)
z  1  10  7z  3
17) 2 x  12  4 x
Directions: Determine whether the following are functions. Circle “yes” or “no”. If “yes”,
determine the domain and range using interval notation. (5 points total)
18) yes
no
19) yes
no
20) yes
no
6
6
6
4
4
4
2
2
2
-5
5
-5
5
-5
5
-2
-2
-2
-4
-4
-4
-6
-6
-6
Domain:__________
Domain:__________
Domain:__________
Range:___________
Range:___________
Range:___________
Directions: Find the function values. For part (c) determine the x-value(s) for which f(x) = 11.
You only need to show your work for part (c). (3 points each)
2
21) f (x)  x  25
22) f (x)  6x  10
a) f(-5) =________
a) f(5)=_________


b) f(10)=_________
c) x =__________
b) f(-2)=_________
c) x =__________
Directions: Let f (x)  x  3 and g(x)  x 15 . Find the following. YOU MUST SHOW
ALL YOUR WORK AND USE APPROPRIATE NOTATION.
(2 points each)
f (5)
23) ( f  g)(5)
24) g(5)
25) 4 f (2)  g(0)
2


27) g( f (x))
26) g(x)  f (x)






29) g
f (5)
28) f
g(5)

30) Directions: For the graph of f(x), find the indicated
function values. Also, find the x value(s) for which f(x) = 2.
(3 points)
f(-5)=______
f(7)=_______
x= _________