A.FGR.9Exponential Function Graphs

Expectations

• A.FGR.9.1

  Use function notation to build and evaluate exponential functions for inputs in their domains and interpret statements that use function notation in terms of a context.

• A.FGR.9.2

  Graph and analyze the key characteristics of simple exponential functions based on mathematically applicable situations.

• A.FGR.9.3

  Identify the effect on the graph generated by an exponential function when replacing $f(x)$ with $f(x)$ + $k$, and $k f(x)$, for specific values of $k$ (both positive and negative); find the value of $k$ given the graphs.

• A.FGR.9.4

  Use mathematically applicable situations algebraically and graphically to build and interpret geometric sequences as functions whose domain is a subset of the integers.

• A.FGR.9.5

  Compare characteristics of two functions each represented in a different way.

Georgia Milestones coverage

• Algebra I (EOC) · Functional & Graphical Reasoning

  Construct and analyze the graph of an exponential function to explain a mathematically applicable situation for which the graph serves as a model; compare exponential with linear and quadratic functions.

  about 12% of the test · 7 points

What mastery looks like

Georgia's Achievement Level Descriptors. The levels are cumulative: each includes the ones before it. Proficient is on grade level.

Beginning

Evaluate an exponential function for a specific value of the domain. Identify a term in a geometric sequence.

Developing

Interpret an exponential function for a given value of the domain in context. Given a table of values or a graph representing an exponential function, identify key features of the function. Given the graph of the exponential function f(x), identify the graph of f(x) + k or kf(x). Identify a rule to describe a geometric sequence.

Proficient

Create an exponential function that represents a real-life situation. Create the graph of an exponential function and identify key features from the graph. Explain the result of replacing the exponential function f(x) with f(x) + k or kf(x). Solve real-life problems involving geometric sequences. Compare key features of two functions presented in different ways (e.g., tables, equations, graphs).

Distinguished

Given an exponential function in a real-life situation, explain the impact of adding a constant (i.e., f(x) + k) or multiplying the output by a constant (i.e., kf(x)) within the context of the situation. Solve real-life problems involving functions in various forms and compare the key features in mathematically applicable situations.