Pre-Calculus 120A

Unit 1: Relations and Functions

Transformations of graphs (translations, stretches, reflections), inverses of relations, radical functions, and the full theory of exponential and logarithmic functions and equations.

• Vertical translations
• Horizontal translations

• Vertical stretches
• Horizontal stretches

• Applying combined translations and stretches
• Writing the equation of a transformed graph

• Reflections in the x- and y-axes
• Reflection in the line y = x
• Inverses of relations and the y = x reflection
• When is the inverse a function?

• Graphing and analyzing radical functions
• Solving radical equations from the graph

• Understanding exponential functions
• Modelling growth and decay with exponentials
• Understanding logarithms
• Graphing exponential and logarithmic functions
• Transformations of exponential and logarithmic graphs

• Product, quotient, and power laws of logarithms
• Solving exponential and logarithmic equations

Unit 2: Trigonometry

Angles in standard position in degrees and radians, the unit circle, the six trigonometric ratios, graphing trigonometric functions, solving trigonometric equations, and proving trigonometric identities.

• Angles in standard position: degrees and radians
• Arc length and the meaning of a radian
• The equation of the unit circle

• Solving problems with the six trigonometric ratios
• Exact values at special angles
• Graphing sine, cosine, and tangent
• Transformed sinusoidal graphs and modelling

• Solving trigonometric equations
• Solving trigonometric equations graphically
• Proving reciprocal, quotient, and Pythagorean identities
• Proving with sum, difference, and double-angle identities