Represent inequalities graphically - Algebra and functions (A-Level Maths)

Inequalities can be represented graphically by drawing the graph, and shading in the appropriate region.

The four possibilities are:

if the inequality is $>$ , draw the graph with a dotted line and shade in the region above the graph;
if the inequality is $<$ , draw the graph with a dotted line and shade in the region below the graph;
if the inequality is $≥$ , draw the graph with a solid line and shade in the region above the graph;
if the inequality is $≤$ , draw the graph with a solid line and shade in the region below the graph.

Important

The solutions to the inequality

f(x) < g(x)

are the values of

x

for which the graph

y=f(x)

is below the graph

y=g(x)

.

The solutions to the inequality

f(x) > g(x)

are the values of

x

for which the graph

y=f(x)

is above the graph

y=g(x)

2.10 Represent inequalities graphically