Using Graphs to Solve Equations and Inequalities (HSC SSCE Mathematics Advanced): Flashcards

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Using Graphs to Solve Equations and Inequalities
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How to find number of solutions graphically

Count the intersection points of the two graphs

What to graph from equation LHS = RHS

Graph y=LHSy = \text{LHS} and y=RHSy = \text{RHS} on same axes

Solutions are which coordinates of intersection points?

The x-coordinates

For LHS>RHS\text{LHS} > \text{RHS}, where is LHS curve?

Above the RHS curve

For LHS<RHS\text{LHS} < \text{RHS}, where is LHS curve?

Below the RHS curve

When to include intersection points in solution

For ≥\geq or ≤\leq inequalities

Shape formed by absolute value function graph

V-shape

Main advantage of graphical approach to equations

Quickly see how many solutions exist and where they are

Two functions from 2x=x+22^x = x + 2

y=2xy = 2^x and y=x+2y = x + 2

Solve ∣2x−5∣≥x+2|2x - 5| \geq x + 2 with intersections at 1, 7

x≤1x \leq 1 or x≥7x \geq 7

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