# Functions

## Function Families: Translations and Reflections

CC.9-12.F.BF.3 – 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.

## Function Familes and Their Connections Including Vertical Shift of an Absolute Value Function

CC.9-12.F.BF.3 – 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.

## Interpret The Rate of Change (Slope) and Intercepts Within The Context of Everyday Life

CC.9-12.F.LE.5 & CC.9-12.S.ID.7 – Interpret the parameters in a linear or exponential function in terms of a context.

## Communicate Real World Problems in Multiple Ways

CC.9-12.F.LE.3 – Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

## Writing Linear Equations

CC.9-12.F.LE.2 – Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

## Writing Equations of a Line Given Two Points

CC.9-12.F.LE.2 – Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

## Slope and Direct Variation

CC.9-12.F.LE.1b – Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

## Determine Minimum, Maximum, Vertex and Zeros Given the Graph

CC.9-12.F.IF.8a – Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

## Solving Absolute Value Inequalities

CC.9-12.F.IF.7b – Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

## Find Zeros of a Function Given the Graph

CC.9-12.F.IF.7a – Graph linear and quadratic functions and show intercepts, maxima, and minima.