### Algebra 2 Fall Semester Review

```Name____________________________________
Algebra 2 Fall Semester Review
Directions: Answer each question as completely as possible. If you do not have enough space, you may use a
separate sheet of paper and attach it.
1) Determine if each relation is function.
____________
____________
___________
____________
2) For 𝑓(𝑥) = 2𝑥 − 9 and 𝑔(𝑥) = 10𝑥, find
𝑓(−3) =__________________
𝑔(𝑓(4)) = __________________
Find the inverse of each function.
3) 𝑓(𝑥) = √𝑥 + 2
5) Solve the following system of equations: {
1
𝑔 (2) = __________________
𝑓(𝑔(−1)) = __________________
4) 𝑓(𝑥) = 𝑥 2 + 6
4𝑥 + 2𝑦 = 20
−2𝑥 − 2𝑦 = 10
−𝑥 − 5𝑦 + 𝑧 = 17
6) Solve the following system of equations using matrices. { −5𝑥 − 5𝑦 + 5𝑧 = 5
2𝑥 + 5𝑦 − 3𝑧 = −10
7) The booster club sold 19 t-shirts, 12 hats, and 8 blankets Monday for \$330. On Tuesday, they sold 7 tshirts, 15 hats, and 12 blankets for \$400. Wednesday they sold 23 hats for \$230. How much is each tshirt, hat, and blanket?
8) Write the system of inequalities for the graph:
9) Graph the system of inequalities on the graph below and list two points in the solution.
1
{𝑦 < 3 𝑥 + 2
𝑥≥5
Solve the following absolute value equations.
1
10) 3 |5𝑥| − 4 = 21
11) |3𝑥 − 2| − 6 = −5
Solve the following absolute value inequalities and graph the solution on the number line.
12) |2𝑥 − 1| < 7
1
13) |3 𝑥| + 5 ≥ 10
State the attributes of the following functions.
14) 𝑓(𝑥) = 2|𝑥 − 3| + 4
15) 𝑓(𝑥) = −|𝑥| − 5
Vertex: ______________
Vertex: ______________
Axis of Symmetry: _______ Max/Min: ___________
Axis of Symmetry: _______ Max/Min: ___________
Domain: _______________ Range: ______________
Domain: _______________ Range: ______________
x-intercept(s): __________ y-intercept: __________
List
the transformations of the following function
x-intercept(s): __________ y-intercept: __________
1
17) 𝑦 = − 2 |𝑥 − 3|
16) 𝑦 = 2|𝑥 + 1| + 1
18)
Graph and state the attributes to the following quadratic functions.
19) 𝑓(𝑥) = 2(𝑥 − 1)2
20) 𝑦 = 𝑥 2 − 2𝑥 + 5
Vertex: ________________
Vertex: ________________
Axis of Symmetry: _______
Axis of Symmetry: _______
Max/Min: ______________
Max/Min: ______________
Domain: _______________
Domain: _______________
Range: ________________
Range: ________________
Write the quadratic function, in vertex form, with the given vertex and passes through the given point.
21) vertex at (−2,5) and passes through (−1,4)
22) vertex at (1,2) and passes through (0,5)
Write the quadratic function that passes through the given points.
23)
x
y
-2
39
3
14
5
32
24) {(0, −32), (5, −17), (6, −20)}
25) The given table represents the height of a bottle rocket as it flies up and returns to the ground. Find a
quadratic function to model the data as a function of x, time in the air. Use the model to determine the
height of the rocket at 3 seconds.
Time
Height
Elapsed (s)
0
2
4
Factor the following expressions.
26) 5𝑚2 𝑛 + 10𝑚𝑛2
27) 𝑦 2 − 81
(ft)
5
11
13
28) 2𝑥 2 + 20𝑥 + 48
29) What are the solutions? 10𝑥 2 + 𝑥 = 3
30) Solve using the quadratic formula. 5𝑥 2 + 2𝑥 = 11
31) The parabola 𝑦 = 3(𝑥 − 5)2 − 6 has vertex (5, −6). If the parabola is shifted 5 units to the right and
up 5 units, what is the equation of the new parabola?
Simplify the expression. Write in 𝒂 + 𝒃𝒊 form.
32) (−9 + 7𝑖) − (11 + 16𝑖)
34) If 𝐴 = [
−2 5
11
]and 𝐵 = [
−4 −6
7
−5
], what is 𝐴 + 𝐵?
2
33) (5 − 11𝑖) + (7 − 15𝑖)
```