*There are standards listed in this section for two reasons.*

*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__

**The Real Number System**

HSN-RN.B. Use properties of rational and irrational numbers and that the product of a nonzero rational number and an irrational number is irrational.

HSN-RN.B.3. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

**Creating Equations**

**HSA-CED.A. Create equations that describe numbers or relationships.**

HSA-CED.A.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

**Reasoning with Equations & Inequalities**

HSA-REI.A. Understand solving equations as a process of reasoning and explain the reasoning.

HSA-REI.A.2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

**HSA-REI.D. Represent and solve [rational] equations and inequalities graphically.**

HSA-REI.D.11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

__Developed and/or Utilized Across Multiple Units__

**Creating Equations**

**HSA-CED.A. Create equations that describe numbers or relationships.**

HSA-CED.A.2. Create [rational] equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

**Interpreting Functions**

**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.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.

**Interpreting Functions**

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

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.★