*There are standards listed in this section for two reasons.*or a function that models a relationship between two quantities, interpret key features of graphs a

*The standards have been modified to be appropriate for this unit. Text in gray font is part of the Michigan K-12 standard but does not apply to this unit. Text in brackets denotes a modification that has been made to the standard.**The standards contain content that is developed and/or utilized across multiple units.*

__Modified For this Unit__

**HSF-IF.C. Analyze functions using different representations.**

HSF-IF.C.7e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

**Building Functions**

**HSF-BF.A. Build a function that models a relationship between two quantities.**

HSF-BF.A.1a. Determine an explicit expression, a recursive process, or steps for calculation from a context.

__Developed and/or utilized across multiple units__

**Quantity**

**HSN-Q.A. Reason quantitatively and use units to solve problems.**

HSN-Q.A.2. Define appropriate quantities for the purpose of descriptive modeling.

HSN-Q.A.3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

**Interpreting Functions**

**HSF-IF.A. Understand the concept of a function and use function notation.**

HSF-IF.A.1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

HSF-IF.A.2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

**Interpreting Functions**

**HSF-IF.B. Interpret functions that arise in applications in terms of the context.**

HSF-IF.B.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

*Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.★*

HSF-IF.B.5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. *For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*★

**HSF-IF.C. Analyze functions using different representations.**

HSF-IF.C.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

**Building Functions**

**HSF-BF.A. Build a function that models a relationship between two quantities.**

HSF-BF.A.1. Write a function that describes a relationship between two quantities.

HSF-BF.A.1b. 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.

**HSF-BF.B. Build new functions from existing functions.**

HSF-BF.B.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.