Exponential Functions Worksheet on Graph Features

About this resource

What's inside this resource

Exponential function characteristics — domain, range, x- and y-intercepts, horizontal asymptote, increasing/decreasing intervals, and end behavior — are analyzed for eight functions per version, four given as graphs and four given as equations such as f(x) = 3^(x-2) - 4 and f(x) = 4^(x+1) + 3. The same characteristics — domain, range, intercepts, and end behavior — are analyzed for quadratic functions in a parallel quadratic characteristics worksheet. Two parallel versions (Version 1 and Version 2) provide different function sets so the worksheet can be reused across two class periods or as a retake, and each version includes a matching, fully worked answer key labeled "KEY" with every domain, range, intercept, asymptote, and end-behavior value filled in using interval and limit notation. The file is credited to "©EightGoneSideways2022" on every page.

Product description

From the author

This is an Exponential Characteristics Worksheet that will give students practice with finding characteristics.

Two versions are included. There are 8 problems on each version.

Students will complete the characteristics for each function that is graphed.

In the classroom

Teaching tips & learning objectives

Learning objectives

Students identify the domain and range of an exponential function from its graph or equation.
Students determine the x- and y-intercepts of an exponential function.
Students identify the horizontal asymptote of an exponential function.
Students describe end behavior of an exponential function using limit notation as x approaches positive and negative infinity.

Teaching tips

Use Version 1 for initial instruction and practice, then assign Version 2 as a retake or parallel second-period assignment, since both versions test the same skill set with different functions.
Have students show scratch work for the equation-based functions (items 5-8) on separate paper, as the worksheet's own directions specify.
Use the KEY pages' interval and limit notation as a model, since students often write asymptote and end-behavior answers inconsistently.

Skills covered

Domain and range identification — students state the domain and range of exponential functions given as graphs or equations.
Intercept-finding — students calculate x- and y-intercepts for exponential equations such as f(x) = 3^(x-2) - 4.
Asymptote identification — students identify the horizontal asymptote (e.g. y = -4) for each exponential function.
End behavior description — students describe end behavior using limit notation as x approaches positive and negative infinity.

Good to know

Questions teachers ask about this resource

Why does the worksheet include two separate versions?

Version 1 and Version 2 present parallel sets of exponential functions testing the same characteristics, so the worksheet can be reused for a second class period or as a retake without repeating the same problems.

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Curriculum

Standards, concepts & topics

Standards

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. a. Graph linear and quadratic functions and show intercepts, maxima, and minima. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. d. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
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.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).

Core concepts

domain and range
x- and y-intercepts
horizontal asymptote
end behavior
exponential functions

Topics

graphing algebra exponential math homework assessment

More to explore

Exponential Function Characteristics Worksheet

What's inside this resource

From the author