# Fractional and Negative Exponents

Simplify using only positive exponents.

**Topic 2: Domain and Discontinuity**

Find the domain of the following functions and describe the discontinuity, if any, as removable or non-removable.

**Topic 3: Solving Inequalities**

Write the following absolute value equations as piecewise equations.

Solve the following by factoring and making appropriate sign charts.

**Topic 4: Special Factorization**

Factor completely.

**Topic 5: Function Transformation**

If f (x) = x^2 −1, describe in words, using correct
mathematical terminology, what the following would do to the

graph of f ( x).

Using the following graph of y = f (x), sketch the following graphs.

**Topic 6: Even and Odd Functions**

Determine if the relation is even, odd or neither analytically.

**Topic 7: Solving Quadratic Equations**

Solve each equation.

**Topic 8: Asymptotes**

Find the equations for all asymptotes, if any exist, for each function.

**Topic 9: Complex Fractions**

Simplify the following.

**Topic 10: Composition of Functions**

If find the following.
For 6-9 state the domain of the resulting

function.

**Topic 11: Solving Rational equations**

Solve each equation for x.

**Topic 12: Logarithmic Function**

Write each expression as a sum and/or difference without exponents.

Write each expression as a single logarithm.

Solve each equation for x.

**Topic 13: Exponential Function**

Solve each of the following for x.

Solve each of the following.

7. Which rate would yield more after 1 year starting with $500?

5 ½ % compounded quarterly 6 ¼ % compounded monthly 9% compounded annually

8. If a population increased from 300,000 to 450,000 from 2001 to 2004, what will the population be in 2007?

9. The half-life of carbon 14 is 5600 years. A piece of
charcoal is found to contain 70% of the carbon 14 that it

originally had. When did the tree from which the charcoal came die?

**Topic 14: Trig Identities**

Establish each trig identity.

**Topic 15: Trig equations**

Solve each equation for x on the interval [0,2π ].

**Topic 16: Limits Algebraically**

Find each limit analytically

9. If find

10. If find

**Topic 17: Limits at Infinity**

Solve each limit without a calculator.