**Title:** We Are Family (Analyze Families of Functions)

**Description:**
Students will be able to analyze and categorize families of functions. This should be a staggered lesson. Once a family of functions is introduced, the graphs can be explored using this lesson. Parent functions for this lesson include square root, absolute value, exponential, and logarithmic.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project, funded by the Malone Family Foundation.

**Standard(s): **

[MA2013] ALT (9-12) 34: Identify the effect on the graph of replacing *f*(*x*) by *f*(*x*) + *k*, *k* *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 illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
[F-BF3]

[MA2013] ALT (9-12) 23: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. [A-CED4]

[MA2013] ALT (9-12) 15: Understand that polynomials form a system analogous to the integers; namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. [A-APR1]