Algebra II – Unit 5 PreTest
Name:
Period_____
Parent Graphs:
1.
2. Describe the transformation of y 
Sketch the graphs:
y  2 x 4  1
y
1
4
x 1
1
x 1  4
4
to y  8 x  6  5
*_________________________
*_________________________
*_________________________
*_________________________
Graph 1
3. Write a system of equations that represents the graph 1
Graph 2
4. Write the exact equation of the graph 2.
Functions:
6. If f ( x)  4  (8  3x) , g ( x)  2 x 2  3x  10
a) find f (2) . Show all work.
7.
(Alg 2 Stand. 24.0)
b) find x if g ( x)  4 . Show all work.
Solution:_______________
Solution:_______________
Find the domain and range:
8. Is {(5, -1), (8, 5), (2, 1), (5, 1)} a function? Explain.
Domain: _________
Function: (Circle)
Yes
No
Range:_________
Why? __________________________________
_______________________________________
Factoring:
16. Factor completely. (CA Alg. 2 Standards 4.0)
a) 15k 2  13k  2
b) 81x 3  1029 y 3
________________
__________________
c) 21a  28b  6ac  8bc
__________________
Absolute Value
11. Solve for x. Show all work. Leave your answer as a fraction (no decimals!). (CA Alg. 2 Standard 12.0)
a)  6 4 x  1  4  14
b) 4 3x  2  3  15
Solution:_______________
Solution:_______________
12. Which inequality(s) could to be added to |2x-3| ? -3 if we wanted to make the solution No Solution?
Be sure to justify your answer.
Inequality Sign: (Circle) >
<
=
Reason: ____________________________________________________________________
Systems:
9. What is the solution to the following system of equations: (CA Alg. 2 Standards 2.0)
 5 x  3 y  6 z  4

 3x  y  5 z  5
Solution:________________
 4 x  2 y  z  13

10. Find the equation of the parabola that passes through the points: (0,1), (2,11), and (-1,8).
(CA Alg. 2 Standards 2.0)
Solution:________________
Quadratics:
13. Find the vertex form of y  3x 2  12 x  8 .
Then state the vertex.
Equation: ________________ Vertex:_____
14. Travis wants to kick a soccer ball into the goal
which is 40 ft away. If the ball follows a
parabolic arc and reaches a maximum height of 8
ft. Find the equation of the parabola that
represents the path of the ball.
Equation:____________________________
Rational Expressions:
15. Simplify each expression. State excluded values.
n 2  36
k  3 k 2  5k  24
a.
b.

k 7
9k  72
5n 2  22n  48
______________________
c.
________________________
x2
7

4 x2
4
d.
x2
b3
7

b2 b4
_________________________
___________________________
Variable Exponents:
17. Simplify:
3
 2 x 6 y 2 

b. 
2 9 
14
x
y


________________
a. (𝑥 7 𝑦 0 𝑧 7 )3
_______________
18. Solve for x:
a. 5 7 x  2  125
b.
1
x 8
 27
_______________
3
________________
8
d. 13x  3  36
x 5
e. 9  1
________________ ______________________
3
c. 7  6 x  4  28
_________________