Ch 1 – Functions and Their Graphs Different Equations for Lines Domain/Range and how to find them Increasing/Decreasing/Constant Function/Not a Function Transformations Shifts Stretches/Shrinks Reflections Combinations of Functions Inverse Functions

Ch 1 – Functions and Their Graphs 1.1 Formulas for lines slope vertical line point- horizontal slope line slope- parallel intercept slopes general perpendicular form slopes

1.2 Functions domain (input) range (output)

1.2 Functions domain (input) range (output)

1.2 Functions Increasing/decreasing/constant on x-axis only (from left to right)

1.2 and 1.3 Functions FunctionsNot functions

1.2 and 1.3 Functions Function or Not a Function? Domain? Range? y-intercepts? x-intercepts? increasing? decreasing?

1.2 and 1.3 Functions Finding domain from a given function. Domain = except: x in the denominator x in radical Can’t divide by zero Can’t root negative

1.4 Shifts (rigid) horizontal shift vertical shift

1.4 Stretches and Shrinks (non-rigid) stretch vertical horizontal shrink stretch shrink

1.4 Reflections In the x-axis In the y-axis If negative can be move to other side, flipped on x-axis. If can’t, flipped on y-axis.

1.5 Combination of Functions

1.6 Inverse Functions

Ch 2 – Polynomials and Rational Functions Quadratic in Standard Form Completing the Square AOS and Vertex Leading Coefficient Test Zeros, Solutions, Factors and x-intercepts Given Zeros, give polynomial function Given Function, find zeros Intermediate Value Theorem, IVT Remainder Theorem Rational Zeros Test Descartes’s Rule Complex Numbers Fundamental Theorem of Algebra Finding Asymptotes

Ch 2 – Polynomials and Rational Functions 2.1 Finding the vertex of a Quadratic Function 1. By writing in standard form (completing the square) 2. By using the AOS formula

2.1 Writing Equation of Parabola in Standard Form

2.2 Leading Coefficient Test Leading Coefficient a Positive Negative Leading exponent n Odd Even

2.2 Zeros, solutions, factors, x-intercepts There are 3 zero (or roots), solutions, factors, and x-intercepts.

2.2 Zeros, solutions, factors, x-intercepts Find the polynomial functions with the following zeros (roots). If the above are zeros, then the factors are: Can be rewritten as

2.2 Zeros, solutions, factors, x-intercepts Find the polynomial functions with the following zeros (roots). Writing the zeros as factors: Simplifying.

2.2 Intermediate Value Theorem (IVT) IVT states that when y goes from positive to negative, There must be an x-intercept.

2.3 Using Division to find factors Long Division Synthetic Division

2.3 Remainder Theorem

2.3 Rational Zeros Test Possible

2.3 Descartes’s Rule Count number of sign changes of f(–x) for number of positive zeros + – = 3 or 1 positive zeros Count number of sign changes of f(–x) for number of negative zeros. – – 0 negative zeros (+) (–) (i)

2.3 Complex Numbers Complex number = Real number + imaginary number Treat as difference of squares.

2.3 Complex Numbers

2.5 Fundamental Theorem of Algebra A polynomial of nth degree has exactly n zeros. has exactly 4 zeros.

2.5 Finding all zeros 1. Start with Descartes’s Rule 2. Rational Zeros Test (p/q) +–i Test a PRZ (or look at graph on calculator).

2.6 Finding Asymptotes Vertical Asymptotes Horizontal Asymptotes Where f is undefined. Set denominator = 0 Degree larger in D, y = 0. O BOBO Degree larger in N, no h asymptotes. N BOTN Degrees same in N and D, take ratio of coefficients.

Ch 3 – Exponential and Log Functions Exponential Functions Logarithmic Functions Graphs (transformations) Compound Interest (by period/continuous) Log Notation Change of Base Expanding/Condensing Log Expressions Solving Log Equations Extraneous Solutions

Ch 3 – Exponential and Log Functions 3.1 Exponential Functions Same transformation as If negative can be move to other side, flipped on x-axis. If can’t, flipped on y-axis. Shifted 1 to right, 2 down. Flipped on x-axis. Flipped on y-axis.

3.1 Compounded Interest Compound by Period Compound Continuously

3.1 Compounded Interest A total of $12,000 is invested at an annual interest rate of 3%. Find the balance after 5 years if the interest is compounded (a) quarterly and (b) continuously.

3.2 Logarithms Used to solve exponential problems (when x is an exponent).

3.2 Logarithms Used to solve exponential problems (when x is an exponent). Change of base

3.3 Logarithms Expanding Log Expressions Condensing Log Expressions

3.4 Solving Logarithmic Equations Solve the Log Equation x in the exponent, use logs

3.4 Solving Logarithmic Equations Solve the Log Equation

3.4 Solving Logarithmic Equations Solve the Log Equation

3.4 Solving Logarithmic Equations Solve the Log Equation

3.4 Solving Logarithmic Equations Solve the Log Equation