Chapter 1
Algebra Review
P
erforming well in calculus is impossible without a solid algebra foundation. Many calculus problems that you encounter involve a calculus concept but then require many,
many steps of algebraic simplification. Having a strong algebra background will allow you
to focus on the calculus concepts and not get lost in the mechanical manipulation that’s
required to solve the problem.
The Problems You’ll Work On
In this chapter, you see a variety of algebra problems:
✓ Simplifying exponents and radicals
✓ Finding the inverse of a function
✓ Understanding and transforming graphs of common functions
✓ Finding the domain and range of a function using a graph
✓ Combining and simplifying polynomial expressions
What to Watch Out For
Don’t let common mistakes trip you up. Some of the following suggestions may be helpful:
✓ Be careful when using properties of exponents. For example, when multiplying
like bases, you add the exponents, and when dividing like bases, you subtract the
exponents.
✓ Factor thoroughly in order to simplify expressions.
✓ Check your solutions for equations and inequalities if you’re unsure of your answer.
Some solutions may be extraneous!
✓ It’s easy to forget some algebra techniques, so don’t worry if you don’t remember
everything! Review, review, review.
Algebra Review
P
erforming well in calculus is impossible without a solid algebra foundation. Many calculus problems that you encounter involve a calculus concept but then require many,
many steps of algebraic simplification. Having a strong algebra background will allow you
to focus on the calculus concepts and not get lost in the mechanical manipulation that’s
required to solve the problem.
The Problems You’ll Work On
In this chapter, you see a variety of algebra problems:
✓ Simplifying exponents and radicals
✓ Finding the inverse of a function
✓ Understanding and transforming graphs of common functions
✓ Finding the domain and range of a function using a graph
✓ Combining and simplifying polynomial expressions
What to Watch Out For
Don’t let common mistakes trip you up. Some of the following suggestions may be helpful:
✓ Be careful when using properties of exponents. For example, when multiplying
like bases, you add the exponents, and when dividing like bases, you subtract the
exponents.
✓ Factor thoroughly in order to simplify expressions.
✓ Check your solutions for equations and inequalities if you’re unsure of your answer.
Some solutions may be extraneous!
✓ It’s easy to forget some algebra techniques, so don’t worry if you don’t remember
everything! Review, review, review.