Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 60542
Writing an Exponential Function From Its Graph
Students are asked to write an exponential function given its graph.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, exponential function, graph
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_WritinganExponentialFunctionFromItsGraph_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problem on the Writing an Exponential Function From Its Graph worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand the basic form of an exponential function.
Examples of Student Work at this Level
The student attempts to write a linear function or an exponential expression.
page 1 of 3 Questions Eliciting Thinking
What is an exponential function? What does the equation of an exponential function look like?
How would you describe this graph? Is it linear?
Instructional Implications
Review the basic form of an exponential function and the meaning of the two parameters, initial amount and growth/decay factor. Provide opportunities for the student to
explore and investigate exponential functions given in context. Include examples of both growth and decay. Explain the significance of points whose coordinates are of the
form (0, x) and (1, x) and demonstrate how these points can be used to write the equation. Encourage the student to relate features of the graph to the parameters in
the equation. Provide additional opportunities for the student to identify the initial amount and the growth/decay factor from given equations and characterize the
equations as modeling either growth or decay. Also, provide opportunities for the student to write exponential functions given a verbal description, a graph, or a table of
values.
If the student wrote a linear function, ask the student to graph the function and compare it to the given graph. Discuss with the student differences in the rates of
increase of the two functions and relate these differences to the forms of the equations.
If needed, review function notation and guide the student to use function notation when writing functions. Provide frequent opportunities to use function notation, so the
student can become familiar and comfortable with its use.
Moving Forward
Misconception/Error
The student is unable to correctly calculate one or both parameters.
Examples of Student Work at this Level
The student correctly identifies the initial amount but:
Calculates the slope of the line containing (0, 0.5) and (1, 3) and identifies it as the growth factor.
Is unable to solve the equation
to find the growth factor.
Questions Eliciting Thinking
What does the value you calculated,
, tell you about this graph?
What are the two important parameters of an exponential function? Can you describe them in words? Which one did you find?
Instructional Implications
Explain the significance of points whose coordinates are of the form (0, x) and (1, x) and demonstrate how these points can be used to write the equation. Provide
additional examples of the graphs of exponential functions and model writing the equation using well-chosen points on a graph. Provide additional examples of graphs of
exponential functions and ask the student to calculate the initial amount and the growth/decay factor and then, write an equation of the form
.
If needed, review function notation and guide the student to use function notation when writing functions. Provide frequent opportunities to use function notation, so the
student can become familiar and comfortable with its use.
Almost There
Misconception/Error
The student makes a minor error in calculating a parameter or writing the function.
Examples of Student Work at this Level
The student:
Correctly calculates the initial amount and growth factor, but neglects to write the exponential function.
Uses function notation incorrectly or not at all.
Writes the exponent as x – 1 rather than x.
Questions Eliciting Thinking
What is the basic form of an exponential function? Did you write the function?
What does function notation look like? What is the difference between f and f(x)?
What happens if you substitute one for x in your function? Will f(1) = 3?
Instructional Implications
page 2 of 3 Provide specific feedback to the student and allow the student to correct the error. Provide additional opportunities to write exponential functions given their graphs.
Consider implementing other MFAS exponential tasks Writing an Exponential Function From a Table (F-LE.1.2), Writing an Exponential Function From a Description (F-LE.1.2),
and What Is the Function Rule? (F-LE.1.2).
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student correctly finds both the initial amount and the growth factor and writes the function as
.
Questions Eliciting Thinking
What do the values in the equation tell you about the exponential equation and its graph?
Can you determine the rate of growth from either your equation or the graph?
If the value of b had been
, what would you know about the equation and its graph?
Instructional Implications
Challenge the student to write an exponential function that contains the points (1, 10) and (2, 20).
Consider implementing other MFAS exponential tasks Writing an Exponential From a Table (F-LE.1.2), Writing an Exponential From a Description (F-LE.1.2), and What Is the
Function Rule? (F-LE.1.2).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Writing an Exponential Function From Its Graph worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.F-LE.1.2:
Description
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description
of a relationship, or two input-output pairs (include reading these from a table). ★
page 3 of 3