Pre-Calculus First Semester Study Guide
Unit 1: Functions
1) Combine functions f(x) and g(x) with addition, subtraction, multiplication, or division
2) Write a composition of functions (𝑓 ∘ 𝑔)(𝑥).
3) Analyze a function (Domain and Range)
4) Write the inverse of f(x) and sketch its graph
5) Analyze the inverse function of f(x) (Domain and Range)
6) Graph a linear, quadratic, cubic, radical, absolute value, and rational function with a
horizontal, vertical translational, vertical stretch, and reflection over x-, and/or y-axis
7) Graph a Piecewise function and/or write its equation. Analyze a Piecewise function
(Domain and Range)
8) Graph and analyze a Greatest Integer function
9) Transform and graph any function given the form: 𝑦 = 𝑎 ∙ 𝑓(𝑥 − 𝑎) + 𝑘
10) Determine a functions symmetry – x-, y-axis, origin, line y = x and verify it algebraically.
Unit 2: Vectors and Triangle Trigonometry
1) Transform vectors with scalar multiples
2) Add and subtract vectors
3) Calculate the norm of vectors and sums of vectors
4) Write vectors in rectangular and polar form
5) Calculate the angle measure between two vectors in degrees
6) Calculate the dot product of a 2-dimensional vector
7) Use the Law of Sines and Cosines to find missing angle or side measures
8) Calculate the area of a triangle without the height
9) Determine the number of possible triangles if using the Law of Sines
Unit 3: Polynomials
1) Solve and/or factor all quadratic polynomials
2) Find all zeros of a polynomial using a graph, technology, or the Rational Root Theorem
3) Factor Polynomials in the forms: a) Sum or Difference of Cubes, and b) Quadratic Form,
to find all possible zeros
4) Graph polynomials written in linear terms demonstrating the correct shape, endbehavior, x-intercepts, and multiplicity
5) Write an equation for a polynomial in standard form given its rational, irrational, and
complex solutions
6) Expand binomials using Pascal’s Triangle and the Binomial Expansion Theorem
Unit 4: Sequence and Series
1) Write explicit and recursive formulas for arithmetic, geometric, and other sequences
2) Write arithmetic, geometric, and other series Sigma Notation
3) Evaluate Finite and Infinite Series when possible