Study Notes
The graph of functions involves understanding different types of graphs such as parabolas, hyperbolas, and trigonometric graphs. Recognizing these graphs helps in sketching and interpreting the behavior of functions.
- Parabola — A curve formed by a quadratic function, either u-shaped or n-shaped. Example: y = ax^2 + bx + c
- Hyperbola — A two-part curve formed by a reciprocal function. Example: y = 1/x
- Cubic Graph — A graph of a cubic function with two turning points. Example: y = ax^3 + bx^2 + cx + d
- Absolute Value Function — A function with a graph that makes sharp turns and is never negative. Example: f(x) = |ax + b|
- Sine Graph — A continuous wave-like graph that repeats every 360º. Example: y = sin(x)
- Cosine Graph — Similar to the sine graph but does not pass through the origin, repeating every 360º. Example: y = cos(x)
- Tangent Graph — A graph with vertical asymptotes, repeating every 180º. Example: y = tan(x)
- Asymptote — A line that a curve approaches but never meets. Example: The line y = 0 is an asymptote for y = 1/x
Exam Tips
Key Definitions to Remember
- Parabola: Curve of a quadratic function
- Hyperbola: Curve of a reciprocal function
- Asymptote: Line a curve approaches but never meets
Common Confusions
- Confusing the shapes of parabolas and hyperbolas
- Misidentifying the turning points in cubic graphs
Typical Exam Questions
- What is the shape of a quadratic graph? A parabola, either u-shaped or n-shaped
- How does a cubic graph differ from a quadratic graph? A cubic graph has two turning points
- What is the period of a sine graph? 360º
What Examiners Usually Test
- Ability to sketch and interpret different types of graphs
- Recognizing the shape of graphs based on equations
- Understanding the properties of trigonometric graphs