Functions

Explore different types of functions and their properties

CAPS Grade 10 Mathematics

Functions describe relationships between variables and are fundamental to mathematics. This section covers linear, quadratic, exponential, and hyperbolic functions. Each topic includes interactive games and quizzes to test your understanding.

Learning Outcomes

  • Understand the definition and notation of functions
  • Identify different types of functions from equations and graphs
  • Determine domain and range of functions
  • Sketch graphs of various functions
  • Apply functions to real-world situations

Function Types

Select a function type to begin your studies.

Linear Functions

y = mx + c — Straight line graphs, slope, intercepts, parallel and perpendicular lines

Explore Linear

Quadratic Functions

y = ax² + bx + c — Parabolas, vertex, axis of symmetry, roots

Explore Quadratic

Exponential Functions

y = a·bˣ — Growth and decay, asymptotes, applications

Explore Exponential

Hyperbolic Functions

y = a/(x + p) + q — Asymptotes, domain, range, branches

Explore Hyperbolic

Function Formulas Summary

Function TypeGeneral FormKey Features
Lineary = mx + cSlope m, y-intercept c, constant rate of change
Quadraticy = ax² + bx + cParabola, vertex (-b/2a, ...), axis of symmetry
Exponentialy = a·bˣAsymptote y = 0, growth (b>1) or decay (0
Hyperbolicy = a/(x + p) + qVertical asymptote x = -p, horizontal asymptote y = q

Quick Check: What do you know?

Test your understanding of functions before diving into the topics.

A) Linear functions have a constant slope
B) Quadratic functions are straight lines
C) Exponential functions always increase
D) Hyperbolic functions have no asymptotes

Hint: Think about the basic properties of each function type.

Key Terms in Functions

Domain Range Slope Intercept Vertex Asymptote Parabola Hyperbola Exponential Linear Quadratic Growth Decay Axis of Symmetry

Study Tips for Functions

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