Mathematics (2019) Grade(s): 8 - Grade 8 Accelerated

MA19.8A.20

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, quadratic, absolute value, and exponential graphs.
  • Methods to use technology, tables, and successive approximations to produce graphs and tables.

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:
  • When two functions are equal, the x coordinate(s) of the intersection of those functions is the value that produces the same output (y-value) for both functions.
  • Technology is useful to quickly and accurately determine solutions and produce graphs of functions.

Vocabulary

  • Functions
  • Successive approximations
  • Linear functions
  • Quadratic functions
  • Absolute value functions
  • Exponential functions
  • Intersection point(s)
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