Exam 4 Sample Problems
Chapter 8
Quadratic Equations, Functions, and Inequalities
1. Solve by completing the square.
a) x2 + 10x = 7
b) x2 − 6x + 10
2. Solve using the quadratic formula: −x2 + 5x = 16.
3. Write in the form y = a(x − h)2 + k, find the vertex, and graph.
a) f (x) = x2 + 4x
b) f (x) = −x2 + 4x − 5
4. Solve the quadratic inequalities.
a) x2 − 3x > 0
b) x2 − 8x ≤ −15
Chapter 9
Exponential and Logarithmic Functions
1. Evaluate (f + g)(x), (f − g)(x), (f g)(x) and (f /g)(x) for the following functions:
g(x) = x2 + x − 1
a) f (x) = 2x + 3
b) f (x) =
√
x+3
g(x) =
1
1
x
2. Assume the functions are one-to-one. Find f −1 (x).
a) f (x) = 5x − 1
b) f (x) = (x + 10)3
c) f (x) = ln (x + 2)
3. Evaluate each expression.
a) log
1
1000
b) log5 125
1
c) ln √
e
4. Graph the functions.
a) f (x) = 2x+1
b) f (x) = log3 x + 4
5. Write as a sum or difference of logarithms. Express powers as factors.
p
a) log4 (x5 4 y + 7)
b) log
xy
z7
6. Write as a single logarithm: log7 x + 2 log7 (x + 1) − log7 4
7. Solve the equations:
a) 72x+1 =
1
7
b) log3 x + log3 (x − 2) = 1
8. Calculate the total interest paid on a 6-year car loan at 7% annual percentage rate interest,
compounded continuously on an initial loan of $19, 000