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

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Using Graphs to Solve Equations and Inequalities
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What can you quickly see from a graph of two functions?

How many solutions exist

What are the solutions to an equation when solving graphically?

The xx-coordinates of intersections

How many solutions does 2x=x+22^x = x + 2 have?

Two solutions

What is one exact solution to 2x=x+22^x = x + 2?

x=2x = 2

How many solutions does 9−x2=1x9 - x^2 = \frac{1}{x} have?

Three solutions

To solve LHS>RHS\text{LHS} > \text{RHS} graphically, find where the LHS curve is:

Above the RHS curve

What is the solution to 2x<x+22^x < x + 2 (approximately)?

−1.7<x<2-1.7 < x < 2

What shape does the graph of y=∣2x−5∣y = |2x - 5| form?

A V-shape

What are the solutions to ∣2x−5∣=x+2|2x - 5| = x + 2?

x=1x = 1 or x=7x = 7

What is the solution to ∣2x−5∣≥x+2|2x - 5| \geq x + 2?

x≤1x \leq 1 or x≥7x \geq 7

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