Problem preview
A-REI.11 Warmup M1-007-A07-V01

Solve equations of the form f(x)=g(x) approximately by finding graph/table intersections.

Count solutions by counting intersections

Problem

Use the graph below to determine the number of solutions to \(f(x)~=~g(x)\).

Big Picture

What this problem is really about

Solutions to the equation correspond to shared graph points, not to the number of curves drawn. We’ll trace the two complete lines and count each distinct place where they have the same horizontal and vertical coordinates. Their slope directions also tell us whether they can meet again after a crossing, which guards against counting a visible line or segment as an additional solution.

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Four variants of this problem type
Curriculum context
Course
Math I
Standard
A-REI.11
Category
Algebra
Domain
Reasoning with Equations and Inequalities
Objective
Solve equations of the form f(x)=g(x) approximately by finding graph/table intersections.
Problem type
Count solutions by counting intersections