Study Notes
Graphs of functions help visualize mathematical relationships. They can be constructed using tables of values and are useful for interpreting different types of functions.
- Parabola — a u-shaped or n-shaped curve representing a quadratic function. Example: The graph of y = x^2 is a parabola.
- Hyperbola — a two-part curve representing a reciprocal function. Example: The graph of y = 1/x is a hyperbola.
- Cubic Graph — a curve with two turning points, representing a cubic function. Example: The graph of y = x^3 is a cubic graph.
- Absolute Value Graph — a graph with sharp turns, representing an absolute value function. Example: The graph of y = |x| has a sharp turn at the origin.
- Sine Graph — a continuous wave-like curve that repeats every 360º. Example: The graph of y = sin(x) is a sine graph.
- Cosine Graph — similar to the sine graph but does not pass through the origin. Example: The graph of y = cos(x) is a cosine graph.
- Tangent Graph — a curve with vertical asymptotes, repeating every 180º. Example: The graph of y = tan(x) is a tangent graph.
- Asymptote — a line that a curve approaches but never meets. Example: The line y = 0 is an asymptote for the graph of y = 1/x.
Exam Tips
Key Definitions to Remember
- Parabola
- Hyperbola
- Cubic Graph
- Absolute Value Graph
- Sine Graph
- Cosine Graph
- Tangent Graph
- Asymptote
Common Confusions
- Confusing the shape of parabolas and hyperbolas
- Misidentifying the turning points in cubic graphs
- Forgetting that absolute value graphs have sharp turns
Typical Exam Questions
- What is the shape of the graph of y = x^2? A parabola
- How does the graph of y = 1/x look? A hyperbola
- Describe the graph of y = x^3. A cubic graph with two turning points
What Examiners Usually Test
- Ability to sketch and interpret different types of graphs
- Understanding of asymptotes and their significance
- Recognition of graph shapes based on function types