Let's Experiment With Graphs of Functions Using Technology!

Subject Area

Mathematics

Grade(s)

7, 9, 10, 11, 12

Overview

This learning activity Let's Experiment With Graphs of Functions Using Technology! will be used during a lesson on identifying 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 using technology, finding the value of k given the graphs, and recognizing even and odd functions from their graphs and algebraic expressions for them.

This activity results from the ALEX Resource Development Summit.

Phase

During/Explore/Explain

Mathematics (2019) Grade(s): 7

MA19.7.22
Solve real-world and mathematical problems involving area, volume, and surface area of two- and three- dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right rectangular prisms.

Vocabulary

Area
volume
Surface area
Two-dimensional figures
Three-dimensional solids
Triangles
quadrilaterals
polygons
Cubes
Right rectangular prisms

Knowledge

Students know:

that volume of any right prism is the product of the height and area of the base.
The volume relationship between pyramids and prisms with the same base and height.
The surface area of prisms and pyramids can be found using the areas of triangular and rectangular faces.

Skills

Students are able to:

find the area and perimeter of two-dimensional objects composed of triangles, quadrilaterals, and polygons.
Use a net of a three-dimensional figure to determine the surface area.
Find the volume and surface area of pyramids, prisms, or three-dimensional objects composed of cubes, pyramids, and right prisms.

Understanding

Students understand that:

two-dimensional and three-dimensional figures can be decomposed into smaller shapes to find the area, surface area, and volume of those figures.
the area of the base of a prism multiplied by the height of the prism gives the volume of the prism.
the volume of a pyramid is 1/3 the volume of a prism with the same base.

Mathematics (2019) Grade(s): 09-12 - Algebra I with Probability

MA19.A1.23
Identify the effect on the graph of replacing $f(x)$ by $f(x) + k$, $k \cdot f(x)$, $f(k \cdot x)$ 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 explain the effects on the graph, using technology as appropriate. Limit to linear, quadratic, exponential, absolute value, and linear \piecewise functions.

Vocabulary

Composite functions
Horizontal and vertical shifts
Horizontal and vertical stretch
Reflections
Translations

Knowledge

Students know:

Graphing techniques of functions.
Methods of using technology to graph functions

Skills

Students are able to:

Accurately graph functions.
Check conjectures about how a parameter change in a function changes the graph and critique the reasoning of others about such shifts.
Identify shifts, stretches, or reflections between graphs.

Understanding

Students understand that:

Graphs of functions may be shifted, stretched, or reflected by adding or multiplying the input or output of a function by a constant value.

Learning Objectives

I can 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 using technology.

I can find the value of k given the graphs.

I can recognize even and odd functions from their graphs.

Activity Details

This activity will be used during a lesson on graphs of functions using technology. Students will complete the activity Let's Experiment With Graphs of Functions Using Technology. Students will complete this activity individually or with a partner.

Assessment Strategies

The activity Let's Experiment With Graphs of Functions Using Technology! can be used to access the student's ability to 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 using technology, to find the value of k given the graphs and to recognize even and odd functions from their graphs.

Variation Tips

The learning activity Let's Experiment With Graphs of Functions Using Technology! can be extended to allow the students to develop their own transformations of functions. Also, it could be used to show how that as the slope of the function gets closer to 0 from the positive direction how the graph will start to get closer to the x-axis and how that as the slope grows farther from 0 in the negative direction that the graph gets closer to the y-axis.

Background / Preparation

Students will need to understand the basic vocabulary of functions and graphs. The students will need to understand the basic operations of the Desmos graphing calculator. The Desmos graphing calculator can be introduced right before this activity or may have been introduced prior to this lesson. The teacher may work the first set of problems together on the projector to show the students how to use the Desmos graphing calculator. The teacher can add the activity to Google Classroom for the students to view. The teacher can copy the activity Let's Experiment With Graphs of Functions Using Technology! for the students to write on and turn in.

Approved Date

2019-08-05

Owner (Author)

kristylacks

Design by Adaptive Theme