High School Math Guide

UTAH CORE STATE STANDARDS for MATHEMATICS

graph, by hand in simple cases and using technology for more complicated cases.  a. Graph linear functions and show intercepts. e. Graph exponential functions, showing intercepts and end behavior. „ „ Standard F.IF.9 Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions) . For example, compare the growth of two linear functions, or two exponential functions such as y =3 n and y =100•2 n . Strand: FUNCTIONS—Building Linear or Exponential Functions (F.BF) Build a linear or exponential function that models a relationship between two quantities ( Standards F.BF.1–2). Build new functions from existing functions (Standard F.BF.3). „ „ Standard F.BF.1 Write a function that describes a relationship between two quantities.  a. Determine an explicit expression, a recursive process, or steps for calculation from a context. b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. „ „ Standard F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Limit to linear and exponential functions. Connect arithmetic sequences to linear func tions and geometric sequences to exponential functions.  „ „ Standard F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, for specific values of k (both positive and negative); find the value of k given the graphs. Relate the vertical translation of a linear function to its y -intercept. Experiment with cases and illus trate an explanation of the effects on the graph using technology. Strand: FUNCTIONS—Linear and Exponential (F.LE) Construct and compare linear and exponential models and solve problems (Standards F.LE.1– 3). Interpret expressions for functions in terms of the situation they model. (Standard F.LE.5). „ „ Standard F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal differences over equal intervals; exponen tial functions grow by equal factors over equal intervals. b. Recognize situations in which one quantity changes at a constant rate per unit inter val relative to another.

SECONDARY MATHEMATICS I | 9