Name:
Algebra 2
Quarter 1 Test Review Packet
Quarter Test Date:
Part 1 – Functions
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Function characteristics – domain, range, increasing, decreasing, zeroes, y-intercept,
minimum, maximum, vertical line test and definition of function
o Domain – all the x-values on a graph; left to right ___ ≤ x ≤ ____
o Range – all the y-values on a graph; low to high ___ ≤ y ≤ ____
o Increasing – highlight where the graph goes UP from left to right and find the Xvalues where it starts and stops
o Decreasing – highlight where the graph goes DOWN from left to right and find
the X-values where it starts and stops
o Zeroes – x-intercepts; where graph crosses x-axis
o Y-intercept – where graph crosses y-axis
o Minimum – lowest y value on graph
o Maximum – highest y value on graph
o Function – every x value has only 1 y value; Vertical Line Test
o F(x) is the same thing as y =
Linear versus nonlinear
Regression – long steps on a calculator!; 4: Add Lists and Spreadsheets; 5: Add Data;
Menu – Analyze – Regression; choose linear or quadratic
Parent functions
Inverse functions – switch the x and y values
1. The data in the table below were collected on five successive Saturdays. They show the
average number of cars entering a shopping center parking lot. The value of t is the number of
minutes after 9:00AM. The value of N is the number of cars that enter the parking lot in the 10
minutes prior to the value of t.
t
20
40
60
80
100 120 140 160 180 200 220 240
N
70 135 178 210 260 280 301 298 284 286 260 195
What is the regression equation?

Using the model, how many cars would be expected to enter the parking lot when t = 265?
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2.
Domain:
Range:
Function? Yes or No
Increasing:
Decreasing:
Local Minimum:
Local Maximum:
Zeroes:
Y-intercept:
3.
Domain:
Range:
Function? Yes or No
Zeroes:
Y-intercepts:
4. Write the mapping function shown below as ordered pairs.
Write the inverse of the function as ordered pairs.
Is the inverse a function? Explain how you know.
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5. Match the function name to the equation. Write the letter in the blank. Then, draw the graph
of the parent function.
1. Quadratic
A. y = |x|
2. Square Root
B. y = x3
3. Cube
C. y = x2
4. Cube Root
D. y = 2x
5. Absolute Value
E. y  x
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F. y  3 x
6. Exponential
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Part 2 – Piecewise Functions and Absolute Value
PIECEWISE Functions
6.
3x  9

f (x)  7

2x  3
a)
b)
c)
d)
e)
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8.
2x 1, x 1
7. f (x)  
3x  4, x 1
x3
3 x 7
x 7
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f(0) =
f(2) =
f(5) =
f(7) =
f(8) =
3 5  x  0

f (x)  2 0  x  3

x 3
5
 x  4, if x  2
9. h( x)  
 2 x  1, if x  2
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10. Draw the following absolute value graphs.
a) y  
1
x  3 1
2
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b) y 
3
x 4
2
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Vertex:
Domain:
Range:
Increasing:
Decreasing:
Zeroes:
Vertex:
Domain:
Range:
Increasing:
Decreasing:
Solving ABSOLUTE VALUE equations
 Get the absolute value by itself first – CAN’T TOUCH THIS! 
 Split into TWO equations!!!! (one positive and one negative)
 IF it looks something like |3x + 1| = 5x where you have that 5x in there, it might be
EXTRANEOUS. Split into 2, then plug both solutions back into the 5x to check.
 IF your problem looks something like |2x – 1| = -6 where the absolute value portion
equals a negative number, there is NO SOLUTION!
11.
3|2x – 7|– 5 = 4
12.
|-2x – 5| = 21
5
13.
|3x – 2| = -10
14.
|3x – 2 | = 11x
Solving ABSOLUTE VALUE inequalities
 Less thAND = sANDwich  write the negative on the left and a < sign
o Shade in middle
 GreatOR  split into 2 inequalities; keep on the same; for the other, switch the inequality
and make it negative
o Shade on outsides
 If you multiply or divide by a negative number, SWITCH the inequality!!!!
 Interval notation
o “AND”  what is the left most number? What is the right most number?
 Ex. (-1, 5]
( ) for < >
[ ] for ≤ ≥
o “OR”  go from - to a number and then from a number to 
 Ex. (-, 3)  [5, )
 Set builder notation {x | _____________}
Solve the inequalities. Graph on a number line. Write in interval and set builder notation.
15.
|7 – 8x| < 3
16.
|3x + 2| – 1 ≥ 10
Interval:
Interval:
Set builder:
Set builder:
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17.
|3x + 4| ≤ 10
18.
|8x + 5| + 3 > 4
Interval:
Interval:
Set builder:
Set builder:
Part 3 – Graphing Quadratics
Graph the following functions. Include the vertex, opening, and axis of symmetry.
19. y = x2 + 2x + 1
Opening: __________
Axis of Symmetry: ____________
Vertex: _______________
x
y
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20. y = (x + 1)(x - 3)
Opening: __________
Axis of Symmetry: ____________
Vertex: _______________
x
y
Practice turning this problem into standard form:
21. y = 2(x + 1)2 – 3
Opening: __________
Axis of Symmetry: ____________
Vertex: _______________
x
y
Practice turning this problem into standard form:
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