MA19.A2.16

Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.16
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 illustrate an explanation of the effects on the graph using technology. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions.

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.

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

Polynomial functions
Trigonometric (sine and cosine) functions
Logarithmic functions
Reciprocal functions
Radical functions
General piecewise functions

Design by Adaptive Theme