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 $y$y values change by the same amount for constant changes in $x$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 $y$y-values.

Here are some examples:

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

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

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

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

Examples

Question 1

Consider the graph of $y=x^2$y=x2.

Loading Graph...

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

Loading Graph...
What is the equation of the axis of symmetry of $y=x^2-2$y=x2−2?

Question 2

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

Complete the table of values for the curve.

$x$x $-4$−4 $-2$−2 $-1$−1

$y$y $\editable{}$ $\editable{}$ $\editable{}$
Use the points in the table to sketch the curve.

Loading Graph...

Question 3