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

MA19.A1.23

Identify the effect on the graph of replacing $f(x)$ by $f(x) + k$, $k \cdot f(x)$, $f(k \cdot x)$ and $f(x + k)$ for specific values of $k$ (both positive and negative); find the value of $k$ given the graphs. Experiment with cases and explain the effects on the graph, using technology as appropriate. Limit to linear, quadratic, exponential, absolute value, and linear \piecewise functions.

Unpacked Content

Knowledge

Students know:
  • Graphing techniques of functions.
  • Methods of using technology to graph functions

Skills

Students are able to:
  • Accurately graph functions.
  • Check conjectures about how a parameter change in a function changes the graph and critique the reasoning of others about such shifts.
  • Identify shifts, stretches, or reflections between graphs.

Understanding

Students understand that:
  • Graphs of functions may be shifted, stretched, or reflected by adding or multiplying the input or output of a function by a constant value.

Vocabulary

  • Composite functions
  • Horizontal and vertical shifts
  • Horizontal and vertical stretch
  • Reflections
  • Translations
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