**Unit 1: Function Families**

**Unit 1 Standards**

**MM1A1. Students will explore and interpret the characteristics of functions, using **

**graphs, tables, and simple algebraic techniques. **

a. Represent functions using function notation.

b. Graph the basic functions *f*(*x*) = *x ^{n}*, where

*n*= 1 to 3,

*f*(

*x*) =

*x*,

*f*(

*x*) = |

*x*|,

and *f*(*x*) = *x*1.

c. Graph transformations of basic functions including vertical shifts, stretches,

and shrinks, as well as reflections across the *x*- and *y*-axes.

d. Investigate and explain the characteristics of a function: domain, range,

zeros, intercepts, intervals of increase and decrease, maximum and minimum

values, and end behavior.

e. Relate to a given context the characteristics of a function, and use graphs and

tables to investigate its behavior.

f. Recognize sequences as functions with domains that are whole numbers.

g. Explore rates of change, comparing constant rates of change (i.e., slope)

versus variable rates of change. Compare rates of change of linear, quadratic,

square root, and other function families.

**MM1G2. Students will understand and use the language of mathematical argument **

**and justification. **

a. Use conjecture, inductive reasoning, deductive reasoning, counterexamples,

and indirect proof as appropriate.

b. Understand and use the relationships among a statement and its converse,

inverse, and contrapositive.**Unit 1 Vocabulary **

- Function
- Function notation
- Input Variable
- Output Variable
- Linear function
- Parabola
- Quadratic Function
- Cubic Function
- Reciprocal Function
- Square Root Function
- Absolute Value Function

**Unit 1 Essential Questions**

- How do I represent functions using function notation?
- How do I graph the basic functions?