Class IX

Non-Linear Graphs

Lesson

Linear Vs Nonlinear

Graphs

A linear relationship is a relationship that has constant rate of change. The gradient is a constant value and the $$y values change by the same amount for constant changes in $$x values.

Linear relationships, when graphed, are STRAIGHT LINES!

This makes anything that is not a straight line nonlinear.

These graphs are all linear.

These graphs are all nonlinear.

Table of Values

As we saw in the previous lesson on tables of values, identifying if a function is linear from a table of values requires us to check for a constant rate of change in the $$y-values.

Here are some examples:

Constant change in $$x and in $$y LINEAR RELATIONSHIP

Constant change in $$x, not a constant change in $$y, NONLINEAR RELATIONSHIP

Constant change in $$x and in $$y LINEAR RELATIONSHIP

Non constant change in $$x, non constant change in $$y. Would need to check if Linear by checking the gradient formula. This in fact is Linear - can you find the rule?

Non constant change in $$x, non constant change in $$y, would need to check using the gradient formula. This is NONLINEAR.

Examples

Question 1

Consider the graph of $$y=x2.

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Which transformation of $$y=x2 results in the curve $$y=x2−2?
widening the curve
A
reflecting the curve about the $$x-axis
B
shifting the curve vertically by $$2 units
C
narrowing the curve
D
shifting the curve horizontally by $$2 units
E
By moving the graph of $$y=x2, sketch a graph of $$y=x2−2.

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What is the equation of the axis of symmetry of $$y=x2−2?

Question 2

Consider the curve whose equation is $$y=(x+4)(x+2).

Complete the table of values for the curve.

$$x $$−4 $$−2 $$−1

$$y $$ $$ $$
Use the points in the table to sketch the curve.

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Question 3