MA19.8A.25

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

MA19.8A.25
Identify the effect on the graph of replacing $f(x)$ by $f(x) + k$, $k \cdot f(x)$, $f (kx)$, 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. Extend from linear to quadratic, exponential, absolute value, and linear \piecewise functions. [Algebra I with Probability, 23, edited]

Unpacked Content

Knowledge

Students know:

Graphing techniques of functions,
Methods of using technology to graph functions.
Techniques to identify even and odd functions both algebraically and from a graph.

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.
Determine when a function is even or odd.

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.
Even and odd functions may be identified from a graph or algebraic form of a function.

Vocabulary

Even and odd functions
Composite functions
Horizontal and vertical shifts
Horizontal and vertical stretch
Reflections
Translations

Design by Adaptive Theme