• Creating Equations
A-CED Create equations that describe numbers or relationships.

MGSE9-12.A.CED.1 Create equations and inequalities in one variable and use them to solve problems.
Include equations arising from linear, quadratic, simple rational, and exponential functions (integer
inputs only).

MGSE9-12.A.CED.2 Create linear, quadratic, and exponential equations in two or more variables to
represent relationships between quantities; graph equations on coordinate axes with labels and scales.
(The phrase “in two or more variables” refers to formulas like the compound interest formula, in which
A = P(1 + r/n)nt has multiple variables.)

GA: HS: Functions
Interpreting Functions
F-IF Analyze functions using different representations.

MGSE9-12.F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Building Functions
F-BF Build a function that models a relationship between two quantities.

MGSE9-12.F.BF.1 Write a function that describes a relationship between two quantities.

MGSE9-12.F.BF.2 Write arithmetic and geometric sequences recursively and explicitly, use them to model situations, and translate between the two forms. Connect arithmetic sequences to linear functions and geometric sequences to exponential functions.

F-BF Build new functions from existing functions.

MGSE9-12.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.
•  Key Vocabulary

Algebra • Average Rate of Change • Coefficient • Continuous • Discrete • Domain • End Behaviors • Equation • Explicit Expression • Exponential Function • Exponential Model • Expression • Factor • Geometric Sequence • Horizontal Translation • Interval Notation • Irrational Number • Natural Numbers • Ordered Pair • Parameter • Range • Rational Number • Real Numbers • Recursive Formula • Reflection • Term • Variable • Vertical Translation • Whole Numbers • X-intercept • Y-intercept