Identify Amplitude (height), Period (length of one cycle), and Phase Shift (horizontal slide). Identities: Use Pythagorean identities ( ) to simplify expressions before graphing. 5. Limits: The Bridge to Calculus
The "Limit" describes the behavior of a function as it approaches a specific point.
Master Precalculus with Limits: A Graphing Approach This guide focuses on mastering functions, trigonometry, and the introduction to calculus through a visual and graphical lens. 1. Master the Library of Functions
Graphing is easier when you view equations as "shifts" of the parent functions. Horizontal Shifts: (Right) or Reflections: (Over x-axis) or (Over y-axis) Scaling: stretches or shrinks the graph vertically. 3. Analyze Polynomial & Rational Functions
Find x-intercepts and determine "multiplicity" (does the graph cross or bounce?). Asymptotes: Vertical: Where the denominator equals zero.
Use the Leading Coefficient Test to see where the graph goes as
If a graph looks weird, plot 3-5 specific points to anchor it.
Compare the degrees of the numerator and denominator. 4. Trigonometry via the Unit Circle Coordinates: Remember
Precalculus With Limits: A Graphing Approach [No Survey]
Identify Amplitude (height), Period (length of one cycle), and Phase Shift (horizontal slide). Identities: Use Pythagorean identities ( ) to simplify expressions before graphing. 5. Limits: The Bridge to Calculus
The "Limit" describes the behavior of a function as it approaches a specific point.
Master Precalculus with Limits: A Graphing Approach This guide focuses on mastering functions, trigonometry, and the introduction to calculus through a visual and graphical lens. 1. Master the Library of Functions Precalculus with Limits: A Graphing Approach
Graphing is easier when you view equations as "shifts" of the parent functions. Horizontal Shifts: (Right) or Reflections: (Over x-axis) or (Over y-axis) Scaling: stretches or shrinks the graph vertically. 3. Analyze Polynomial & Rational Functions
Find x-intercepts and determine "multiplicity" (does the graph cross or bounce?). Asymptotes: Vertical: Where the denominator equals zero. Identify Amplitude (height), Period (length of one cycle),
Use the Leading Coefficient Test to see where the graph goes as
If a graph looks weird, plot 3-5 specific points to anchor it. Limits: The Bridge to Calculus The "Limit" describes
Compare the degrees of the numerator and denominator. 4. Trigonometry via the Unit Circle Coordinates: Remember