A lot of this is stolen from the Midterm 1 review sheet, because it's the same stuff as you should have reviewed the first time. Emphasis on the final will be on the last few weeks -- logs and exponentials in particular, but also polynomials and rational functions. Domains, as always, will show up, because we love them.
Use your midterms as a guide for studying. Once I've figured out how the final will look, I'll publish a version of the final I was going to use as a further study guide. It, unsurprisingly, looks a lot like the midterms. I'll additionally highlight some of my favorite homework problems some time before Friday -- link to appear on the main web page.
Please come see me or send e-mail or call if you have questions. That's what I'm here for. We'll schedule official review sessions and things for next week soon.
Section 1.1:
- Number Line
- Interval Notation: {a, b}, [a, b], {a, b], [a, b)
- Absolute Value
- Distance on the Number Line: d = |a - b|
Section 1.2:
- Factoring Quadratics: (x + a) (x + b) = 0
- Completing the Square: x2 + 3x = 17
- Quadratic Formula (Memorize!)
- Discriminant and Number of Real Solutions
- Absolute Value Equations (1.2A): |x + 3| = 2
Section 1.3:
- Distance Formula (Memorize!)
- Midpoint Formula
Section 1.4:
- Slope of a Line (Rise Over Run)
- Slope-Intercept Form of a Line: f(x)=mx+b
- Parallel and Perpendicular Lines (Slopes!)
Section 3.1:
- Definition of a Function (Memorize!)
- Domain and Range of a Function (Definitions, too!)
- Vertical Line Test
Section 3.2:
- Functional Notation: f(x)
- Difference Quotient
Section 3.3:
- Graphing Functions
- Catalog of Basic Functions
- Reading Graphs
Section 3.4:
- Horizontal Graph Shifts: f(x + c)
- Vertical Graph Shifts: f(x) + c
- Stretching and Squishing Graphs: cf(x)
- Reflecting Graphs About the X-axis: -f(x)
- Reflecting Graphs About the Y-axis: f(-x)
Section 3.5:
- Sums of Functions: (f+g)(x)
- Products of Functions: (fg)(x)
- Quotients of Functions: (f/g)(x)
- Composition of Functions: (f o g) (x)
- Finding Domains of ALL of these
Section 3.7:
- 1-1 Functions/Horizontal Line Test
- Finding Inverse Functions
- Restricting Domains to Make Functions 1-1
Section 4.1:
- "Standard Form" of a Quadratic: f(x) = a(x-h)^2 + k
- Finding Vertex of a Parabola
- Sketching Quadratics using Standard Form
Section 4.2:
- Polynomial Long Division
- Factor/Remainder Theorems
- Number of Roots a Polynomial can have
Section 4.4:
- Asymptotic Behavior of Polynomials (when |x| is large)
- Multiplicity of Roots and how it affects graphs
- Local Extreema
- Using all of these to sketch graphs of polynomials without evaluating
Section 4.5:
- Finding Vertical Asymptotes and Holes when they exist
- Finding Horizontal Asymptotes (All 3 cases)
- Sketching Graphs by plugging in numbers close to asymptotes
Section 5.1:
- Rules for Exponents
- Graphs of Roots -- cube root, in particular
- Solving Equations involving exponents
Section 5.2:
- General Form Exponential Function: B(t) = Pb^(kt)
- How to Fill in General Form from given information
- Graphs of Various Exponentials -- 2^x and (1/2)^x come to mind
Section 5.2A:
- Compound Interest Formula: B(t) = P(1+(r/n))^(nt)
- Continuously Compounded Interest -- B(t) = Pe^(rt)
- How to use these to calculate values and rates
Section 5.3:
- Definition of Logarithms
- Domain of Logarithm Function
- Graphs of Logarithms
Section 5.4:
- Logarithm Rules
- Rewriting Expressions using only one logarithm
Section 5.5:
- Using Logarithms to Solve for Exponents in equations
- Setting up Equations that Logarithms will solve
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