Mathematics (2019) Grade(s): 09-12 - Algebra I with Probability

MA19.A1.19

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 $f(x) = g(x)$.

Unpacked Content

Knowledge

Students know:
  • Defining characteristics of linear, polynomial, absolute value, and exponential graphs.
  • Methods to use technology and tables to produce graphs and tables for two functions.

Skills

Students are able to:
  • Determine a solution or solutions of a system of two functions.
  • Accurately use technology to produce graphs and tables for linear, quadratic, absolute value, and exponential functions.
  • Accurately use technology to approximate solutions on graphs.

Understanding

Students understand that:
  • By graphing y=f(x) and y=g(x) on the same coordinate plane, the x-coordinate of the intersections of the two equations is the solution to the equation f(x) = g(x)

Vocabulary

  • Functions
  • Linear functions
  • Absolute value functions
  • Exponential functions
  • Intersection
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