College Algebra

College Algebra

Name
Directions: Show all of your work. No work = No credit.
1. Find (f ± g)(x) and (g ± f)(x) for the given functions:
f(x) = 2×2 ¡ 9; g(x) = 7x + 1
2. Given that f(x) = (x + 2)3:
a) Find and equation of the inverse function, f¡1(x).
b) Verify that your equation is correct by showing that (f ± f¡1)(x) = x and (f¡1 ± f)(x) = x
3. Write each equation in its equivalent logarithmic form:
a) 152 = x
b) 8y = 300
4. Write each equation in its equivalent exponential form. Then ¯nd the missing variable:
a) log2 x = 4
b) log6 216 = y
5. Use the properties of logarithms to expand each expression as far as possible:
a) log2(a5b8)
b) logb µx2y
z2 ¶
6. Use the properties of logarithms to condense each expression into the logarithm of a single
expression:
a) 2 logb x + 3 logb y
b) 2 ln x ¡ 1
2 ln y
7. Solve each equation below:
(a) 32x+1 = 27
(b) log4(x + 2) ¡ log4(x ¡ 1) = 1
8. If $4000 is placed in a savings account paying 5% interest compounded continuously, ¯nd the
time needed for the account to grow to $10,000. (HINT: Use the formula A = Pert)
9. Give the center and radius of the circle (x ¡ 2)2 + (y + 4)2 = 16 and then graph it.
10. Graph the ellipse
(x ¡ 4)2
4
+
y2
25
= 1
11. Use the vertices and asymptotes to graph the hyperbola 4×2 ¡ 25y2 = 100.
12. Find the sum P4
i=1(2i2 + 8)
13. Write the ¯rst six terms of the arithmetic sequence with a1 = 7 and d = ¡4.
14. Find the sum of the ¯rst 25 terms of the arithmetic sequence 7,19,31,43,….
15. Write the formula for the general term, an, of the geometric sequence 3,15,75,375,…. Then ¯nd
a8, the eighth term of the sequence.
BONUS: Find the sum of the in¯nite geometric sequence 3 ¡ 1 + 1
3 ¡ 1
9 + :::.