# Mid-Term Review

```Pre-Calculus
Mid-Term Exam Review
Name ___________________________________ Pd ___
Chapter 1: Functions
Determine whether the following relations are functions.
1) {(0, -3), (4, 6), (0, 4)}
2) {(5, 3), (2, 3)}
3)
4)
For f(x) = 2x2 – x and g(x) = x + 6, find the following values.
5) f(g(x))
6) g(f(x))
7) f(t-3)
8) g(f(3))
Determine whether the given function is even, odd, or neither.
9)
10)
11)
12)
For each graph below, determine the domain, range, y-intercept, zeros (x-intercepts), continuity, maximums and
minimums, intervals of increasing and decreasing, asymptotes, and end behavior. If the characteristic is not present,
write N/A.
13)
14)
15)
𝒙 + 𝟐 𝒊𝒇 𝒙 ≤ 𝟎
Use the piecewise function 𝒇(𝒙) = {
for questions 16-19.
−𝒙𝟐 𝒊𝒇 𝒙 &gt; 𝟎
16) Graph the function on the grid provided.
17) Find f(-2)
18) Find f(0)
19) Find f(1)
If f(x) = x2 is the parent graph, describe how the following graphs are transformed.
20) (x + 2)2 - 4
21) –x2
22) x-2
23) x2 + 5
d) c
24) Sketch the following parent functions on the grid provided.
a) x
b) x2
c) x3
e) log 𝑏 𝑥
f) √𝑥
g) 𝑥
1
h) bx
Chapter 2
For each polynomial, determine whether the degree is even or odd AND whether the leading coefficient is positive or
negative.
25)
26)
27)
28)
Determine the horizontal asymptote(s), the vertical asymptote(s), and the hole(s) for the following functions.
29) 𝑓(𝑥) =
𝑥+4
−2𝑥−6
30) 𝑔(𝑥) =
2𝑥+6
𝑥 2 +𝑥−6
31) ℎ(𝑥) =
𝑥 3 −𝑥 2 −6𝑥
−3𝑥 2 −3𝑥+18
Solve each equation.
32) √2𝑥 − 7 + 3 = 𝑥
33)
34)
35)
Chapter 3
Evaluate each logarithm.
36)
37)
38)
39)
Solve each equation. (ISOLATE!!!)
40) 2𝑒 𝑥 + 4 = 10
41) 3x-1 = 25
42) 4log 4x – 1 = 7
43) 5 ln x = 50
44) In 2008, the raccoon population in a certain area was 15,000. The number of raccoons decreases exponentially at a
rate of 8% per year. Predict the population in 2014.
45) Ellen is investing \$1,500 in an account that earns an APR of 5% interest.
a) How much is the account worth in 15 years if it is compounded monthly?
b) How much is the account worth in 15 years if it is compounded daily?
c) How much is the account worth in 15 years if it is compounded continuously?
46) The city of Sugar Land has been experiencing rapid growth as shown in the table below.
Year
1980
1981
1982
1983
1984
1985
Population
18,940
21,150
23,490
27,570
29,610
35,480
a) Find an exponential regression equation that models this data.
b) Use the exponential regression equation to predict the population in 1990.
c) Use the exponential regression equation to predict when the population will reach 100,000.
```