CCSS.Math.Content.HSA-REI.D.11
The standard
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
Common Core State Standards for Mathematics
What this standard means
Students need to connect an equation to a graph. If two functions have the same output at the same input, their graphs meet there. The x-value of that meeting point is a solution. They also need to estimate solutions from graphs, tables, or repeated zooming and checking.
Mastery means students can explain the connection in words, not just point at a calculator screen. They can handle different function types and decide when an answer is approximate. Common stuck points are reading the y-value instead of the x-value, missing multiple intersections, and trusting a graph window that hides a solution.
Ways to teach it
- Have students graph two functions on Desmos, place movable points at intersections, and record each x-value as a solution.
- Ask students to explain why solving 2x+3=x^2 means finding where a line and parabola meet.
- Give a quick exit ticket with one graph of two functions and ask for all approximate solutions.
- Use a phone plan comparison table and graph to find when two monthly cost formulas are equal.
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