Name
Date:
Algebra 2 & Trigonometry
Midterm Review Sheet #4
YOU MUST SHOW ALL WORK, EVEN ON MULTIPLE CHOICE QUESTIONS, IF YOU
WANT TO EARN FULL CREDIT!
1. Solve for x: x2 – 36 > 0
x2 – 1
2. Solve for x: 3x + 4 < 0
x–5
3. Solve for x using the quadratic formula: 2x2 - 9x + 2 = 0
4. Solve for x by completing the square: x2 + 9x – 7 = 0
5. Solve for x: x4 – 18x2 + 81 = 0
6. Solve for x: 2x3 + 14x2 – 10x = 0
7. State if the relation is a function, explain your answer. {(7, -2), (4, -2), (1, 3), (0, 9), (4, -1),
(2, 9)}
8.
Solve for x: 2 x  6 x  1  3
9. Given f(x) = 3x – 8, g(x) =
a. f(-9)
b. g(12)
c. h(-1)
d. g(f(6))
e. h(f(g(4)))
f.
f(g(x))
g. h(f(x))
x
 5 and h(x) = x2 – 5x + 1, find:
2
10. Sketch each equation (without using a calculator). State the domain and range of each
equation, then state whether the equation a function.
a. y = 4x – 9
b. y = x2 – 8x + 3
c. x2 + y2 = 1
e.
y=
x7
11. Write the inverse of each of the following functions:
d. y = -|x| + 5
f. f(x) = 2x + 2
a. f(x)= -8x + 1
12. Using the composition of functions, prove
b. g(x) = x3 + 7
f ( x) 
x2
2
and g ( x ) 
are inverse
x
x 1
functions.
13. Given f(x) = x2, write the equation that would shift the graph of the equation 2 units to the
right.
14. Given g(x) = |x|, write the equation that would shift the graph of the equation 3 units to the
left and 2 units down.
15. Consider the graph of the function f(x) shown:
On the same set of axes, sketch the graph of the function f(-x).
16. The graph of the function below represents f(x). On the axes to the right, sketch the graph
of the function g(x) = f(x – 3) + 2
17. Simplify.
5 – 7i
3 + 8i
18. Simplify. 4i23 + 8i67 – 3i100 + 2i45
19. Given A = -4 + 7i and B = 2 + -9i, graph A, B and A + B on the grid provided.