Functions & Graphs

Success Criteria

At the end of this chapter, students are able to:

  1. Sketch the graphs of power functions.

  2. Draw the graphs of the sum of simple power functions.

  3. Draw the graphs of exponential functions.

  4. Find the gradient of a curve by constructing a tangent to the curve.

  5. Approximate a solution to an equation using the intersection of 2 graphs (AO2).

  6. Intepret the value of a gradient in a given context (AO3).

  7. Explain why an extrapolated value may not be accurate (AO3).

Introduction to Functions

A function is a relationship that connects an input, x, to an output, f(x).

Functions can be classified by the nature of the formulas that define them. In this site, you can play around with the following types of functions and observe how the constants affect the shape of their respective graphs:

  1. Quadratic Functions: f(x) = ax2 + bx + c

  2. Power Functions: f(x) = axn

  3. Exponential Functions: f(x) = abx

  4. Trigonometric Functions: f(x) = a sin(bx) + c ; and f(x) = a cos(bx) + c

Extension of Learning

For a summary of the shapes of different functions, check out 降龙十八Graphs (上) and 降龙十八Graphs (下).

For a more in-depth understanding of functions, click here.