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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

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.