ALEX Learning Activity

  

Radical Graphs Matter

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  This learning activity provided by:  
Author: Susan Honeycutt
System:Blount County
School:Locust Fork High School
  General Activity Information  
Activity ID: 2543
Title:
Radical Graphs Matter
Digital Tool/Resource:
Graphing Calculator/Desmos.com
Web Address – URL:
Overview:

Students will graph radical functions in the coordinate plane and identify key features. Students will be sure to label the axes and scale of their graphs. Students will identify the domain and the range of each function from the graph of the function.  

This activity results from the ALEX Resource Development Summit.
  Associated Standards and Objectives  
Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability
30. 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 piecewise-defined functions, including step functions and absolute value functions.

c. Graph exponential functions, showing intercepts and end behavior.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given a symbolic representation of a function (including linear, quadratic, absolute value, piecewise-defined functions, and exponential,
  • Produce an accurate graph (by hand in simple cases and by technology in more complicated cases) and justify that the graph is an alternate representation of the symbolic function.
  • Identify key features of the graph and connect these graphical features to the symbolic function, specifically for special functions:
      quadratic or linear (intercepts, maxima, and minima) and piecewise-defined functions, including step functions and absolute value functions (descriptive features such as the values that are in the range of the function and those that are not).
    1. Exponential (intercepts and end behavior).
Teacher Vocabulary:
  • x-intercept
  • y-intercept
  • Maximum
  • Minimum
  • End behavior
  • Linear function
  • Factorization
  • Quadratic function
  • Intercepts
  • Piece-wise function
  • Step function
  • Absolute value function
  • Exponential function
  • Domain
  • Range
  • Period
  • Midline
  • Amplitude
  • Zeros
Knowledge:
Students know:
  • Techniques for graphing.
  • Key features of graphs of functions.
Skills:
Students are able to:
  • Identify the type of function from the symbolic representation.
  • Manipulate expressions to reveal important features for identification in the function.
  • Accurately graph any relationship.
Understanding:
Students understand that:
  • Key features are different depending on the function.
  • Identifying key features of functions aid in graphing and interpreting the function.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGI.30.1: Define piecewise-defined functions and step functions.
ALGI.30.2: Graph functions expressed symbolically by hand in simple cases.
ALGI.30.3: Graph functions expressed symbolically using technology for a more complicated case.

a.
ALGI.30.4: Graph quadratic functions showing maxima and minima.
ALGI.30.5: Graph quadratic functions showing intercepts.
ALGI.30.6: Graph linear functions showing intercepts.

b.
ALGI.30.7: Define square root, cube root, and absolute value function.
ALGI.30.8: Graph piecewise-defined functions.
ALGI.30.9: Graph step functions.
ALGI.30.10: Graph cube root functions.
ALGI.30.11: Graph square root functions.
ALGI.30.12: Graph absolute value functions.

c.
ALGI.30.13 Identify exponential numbers as repeated multiplication.
ALGI.30.14 Rewrite exponential numbers as repeated multiplication.

Prior Knowledge Skills:
  • Demonstrate how to plot points on a coordinate plane using ordered pairs from a table.
  • Graph a function given the slope-intercept form of an equation.
  • Recognize the absolute value of a rational number is its' distance from 0 on a vertical and horizontal number line.
  • Define absolute value and rational numbers.
  • Recall how to plot ordered pairs on a coordinate plane.
  • Name the pairs of integers and/or rational numbers of a point on a coordinate plane.
Alabama Alternate Achievement Standards
AAS Standard:
M.A.AAS.12.30 Given the graph of a linear function, identify the intercepts, the maxima, and minima.

Learning Objectives:

I can graph radical functions expressed symbolically and show key features of the graph.
  Strategies, Preparations and Variations  
Phase:
During/Explore/Explain
Activity:

The student(s) will be given a radical function to graph by hand on graph paper. The student is to divide their paper in half and then in half again, this will give them creases to draw lines to divide their paper into four parts. In the top left quadrant of the paper, students can draw and label an x-y coordinate plane. Students can then make a table of values by plugging values in for x and finding y (or f(x)) of the first function. Then, they will plot those points (ordered pairs) on the coordinate plane. After they have plotted four or five points, they should connect the points. Then they can input the function into their graphing calculators or Desmos (the digital resource) and confirm that they have graphed the function correctly. After students confirm that they have graphed the function correctly, they can state the domain and range of the function. They should also talk about the end behavior of the function, as well as the solutions of the function. They can partner talk or this can be written down and turned in to the teacher. After the student has graphed one function correctly, they can then use the other three sections of their paper to graph other functions for practice or different variations of radical functions.

Desmos Instructions:  Type in the URL: www.desmos.com. This will take you to the website. Click on start graphing to open the graphing calculator. Type in the function and Desmos will graph the function. You can click on the drop-down arrow in the bottom left of your screen to access the keyboard. On the right side, you will find special features under the functions tab. You can get to letters by clicking the ABC button. There is no need to type in the y= or f(x)  part, just the function part.  
Assessment Strategies:

The teacher will use the students' ability to demonstrate their knowledge of graphing radical functions and of showing key features of the graphs during the activity to determine mastery of the standard. 
Advanced Preparation:

The teacher will need to prepare a list of radical functions and mixed radical functions. The first few problems need to be square roots and mixed roots, like cubed roots, fourth roots, fifth roots, etc.

Students will need a graphing calculator, Chromebook/laptop, or computer.  

Students will need graph paper, rulers, and possibly colored pencils.
Variation Tips (optional):

Students need basic graphing skills such as being able to graph points and lines.

Students can graph different roots, not just square roots. The larger the root the harder it is to make it fit on graph paper without changing the scale of the graph.
Notes or Recommendations (optional):

ALCOS 2019

20. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise
functions.
a. Graph polynomial functions expressed symbolically, identifying zeros when suitable
factorizations are available, and showing end behavior.
b. Graph sine and cosine functions expressed symbolically, showing period, midline, and
amplitude.
c. Graph logarithmic functions expressed symbolically, showing intercepts and end
behavior.
d. Graph reciprocal functions expressed symbolically, identifying horizontal and vertical
asymptotes.
e. Graph square root and cube root functions expressed symbolically.
f. Compare the graphs of inverse functions and the relationships between their key
features, including but not limited to quadratic, square root, exponential, and logarithmic
functions.
  Keywords and Search Tags  
Keywords and Search Tags: coordinate plane, domain, end behavior, graph, radical functions, range