Transforming Functions

GreenMaths, Adam Cooley, Jun 28, 2016

Transforming linear, quadratic and exponential functions. Investigate the effect of changing the equation for each of these functions.

Table of Contents

  1. Linear Functions
    1. Transformation of Linear Functions
  2. Quadratic Functions
    1. Transformation of Quadratic Functions 1
    2. Transformation of Quadratic Functions 2
    3. Transformation of Quadratic Functions 3
  3. Exponential Functions
    1. Transformations of Exponential Functions 3
    2. Transformations of Exponential Functions 1
    3. Transformations of Exponential Functions 2

1.

Linear Functions

  • 1. Transformation of Linear Functions

1.1.

Transformation of Linear Functions

Linear equations can be transformed by changing either the x -coefficient or the constant term.[br][br]Use this applet to see the effect of each change and relate this to a linear equation in the form [i]y[/i] =m[i]x[/i] + c[br][br]Turn the trace on to see copies of the line when you move the slider.
Note in these examples of Linear Equations [i]y[/i] is the subject of the equation. This is called the "slope intercept" form of a linear equation must be written with just [i]y[/i] on the left hand side.[br][br]The same is true for linear functions - f([i]x[/i]) =m[i]x[/i] + c - this is essentially the same as above but just uses a different notation.
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2.

Quadratic Functions

  • 1. Transformation of Quadratic Functions 1
  • 2. Transformation of Quadratic Functions 2
  • 3. Transformation of Quadratic Functions 3

2.1.

Transformation of Quadratic Functions 1

Move the slider to change the coefficient of x squared.[br]You can see the effect of this by comparing the blue graph to the graph of x squared which is red.[br]Use the buttons to show the table and to turn "Trace On" - you will then see copies of the graph as you move the slider.
Transformation of Quadratic Functions 1
Examine the values of a times x squared in the table as you move the slider. A common mistake is to multiply [i]x[/i] by a first and then square - be careful.
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2.2.

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2.3.

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3.

Exponential Functions

  • 1. Transformations of Exponential Functions 3
  • 2. Transformations of Exponential Functions 1
  • 3. Transformations of Exponential Functions 2

3.1.

Transformations of Exponential Functions 3

This applet investigates simple Exponential Functions where the base number is two or three. Move the slider to change the value of [i]c[/i], the constant added to the exponential function. You can see the effect of this by comparing the blue graph to the graph of the simple exponential function which is red. Use the buttons to show the table and to turn "Trace On" - you will then see copies of the graph as you move the slider.

Examine the values in the table as you move the slider. What effect does changing [i]c[/i] have on the graph? What effect does changing the base number have?
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3.2.

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3.3.

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