Name: _________________________________ Period: _____ Date: _________________
Chapter 2: Study Topics
2-1: Power and Radical Functions
 Power/Monomial Functions
o Power Functions:
 f (x)  ax n , where a and n are nonzero constant real numbers.
o Monomial Functions:
 f (x)  a or f (x)  ax n , where a and n are nonzero constant real numbers.
o Domain (interval notation)

o Range (interval notation)
o Intercepts (ordered pair)
o End Behavior (limit notation)
o Continuity (interval notation)
o Increasing/Decreasing (interval notation)
 Radical Functions (Fractional Exponents)
1
n
o f (x)  x  x where n is a positive integer
o Domain (interval notation)
o Range (interval notation)
o Intercepts (ordered pair)

o End Behavior (limit notation)
o Continuity (interval notation)
o Increasing/Decreasing (interval notation)
 Solving Radical Equations
o Isolate the radical expression.
o Square both sides (inverse of the square root)
o Check for extraneous solutions!
n
2-2 Polynomial Functions
 Let n be a nonnegative integer and let a0 ,a1,a2 ,...,an1,an be real numbers with an  0 .
Then, f (x)  an x n  an1 x n1  ... a2 x 2  a1 x  a0
 Leading Term Test
o Degree of function – odd/even


o Leading coefficient – positive/negative

o GIVES US END BEHAVIOR OF THE FUNCTION
 Zeros and Turning Points
o Degree: how many roots
o Degree – 1: how many turning points
 Find Zeros
o Factor
o Quadratic Formula
 Repeated Zeros
o Multiplicity of a zero
o Odd – graph crosses x-axis
o Even – graph is tangent to x-axis
2-3 The Remainder and Factor Theorems
 Dividing Polynomials
o Long Division
o Synthetic Division
 The Remainder Theorem
o If a polynomial f(x) is divided by x – c, the remainder is r = f(c).
 The Factor Theorem
o A polynomial f(x) has a factor (x – c) if and only if f(c) = 0.
2-4 Zeros of Polynomial Functions (use study guide provided for the quiz)
 The Fundamental Theorem of Algebra + Corollary
 Descartes’ Rule of Signs
 Rational Root Test
 Upper and Lower Bound Test
 Linear Factorization
 Conjugate Pair Theorem
2-5 Rational Functions
 The quotient of two polynomial functions.
a(x)
f (x) 
, b(x)  0
b(x)
 Domain
o All real numbers except where the denominator equals zero
 Vertical Asymptote

o Check for common factors
o Set the (remaining) denominator equal to zero
 Horizontal Asymptote
o THERE CAN ONLY BE ONE HORIZONTAL ASYMPTOTE!
o If the degree of the numerator is smaller than the degree of the denominator, then
the horizontal asymptote is at y = 0.
o If the degree of the numerator is equal to the degree of the denominator, then the
horizontal asymptote is the ratio of the leading coefficients.
o If the degree of the numerator is larger than the degree of the denominator, then
there are no horizontal asymptotes.
 Slant Asymptote
o If the degree of the numerator is larger than the degree of the denominator by 1,
then there is a slant asymptote.
o Divide the rational function – the equation of the slant asymptote is the quotient.
 Holes
o A hole occurs when the numerator and the denominator have a common factor.
 X-Intercept
o Set the numerator equal to zero
 Solving Rational Equations
o Factor all the denominators.
o Find the LCD (Least Common Denominator).
o Multiply the entire equation by the LCD to clear the fractions (remember to
multiply each term in the equation).
o Solve the simple equation.
o CHECK FOR EXTRANEOUS SOLUTIONS!
Practice Problems

Worksheets used since the beginning of school!

Section 2.1-2.2 Quiz

Section 2.3 Quiz

Section 2.4 Quiz

Homework Problems:
o 2-1: # 1-4, 9, 10, 17, 18-21, 44, 45, 47, 48, 49, 52, 53, 63-65
o 2-2: # 1-8, 11-19 (odd), 23-41 (odd), 50-79 (odd),
o 2-3: # 1, 3, 5, 9, 15, 17, 19, 21, 23, 25, 27, 28, 53-56
o 2-4: # 11, 13, 15, 18, 19, 24, 27, 29, 33, 35, 43, 45, 49, 51
o 2-5: # 1-8, 33-41 (odd)

Additional Textbook Problems:
o P.149-151: # 11 – 63
o P.153 (Practice Test): Omit #19