ALEX Classroom Resource

  

Analyzing the Graphs of Functions

  Classroom Resource Information  

Title:

 Analyzing the Graphs of Functions

URL:

 https://www.ck12.org/c/calculus/analyzing-the-graphs-of-functions/lesson/Analyzing-the-Graphs-of-Functions-CALC/?referrer=concept_details

Content Source:

 Other
CK-12
Type: Informational Material

Overview:

Given a set of information on the key properties of a function, you can sketch the graph. Before we proceed, make an attempt to summarize what you think are key properties. Often, the key properties of a function are not all presented to you directly but must be determined from the information at hand.

This informational material will explain how to analyze graphs of functions and identify the graph's key features. The article includes many examples of graphs and functions related to this concept. Practice questions with a PDF answer key are provided.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 9-12
Mathematical Modeling
15. Use regression with statistical graphing technology to determine an equation that best fits a set of bivariate data, including nonlinear patterns.

Examples: global temperatures, stock market values, hours of daylight, animal population, carbon dating measurements, online streaming viewership

a. Create a scatter plot with a sufficient number of data points to predict a pattern.

b. Describe the overall relationship between two quantitative variables (increase, decrease, linearity, concavity, extrema, inflection) or pattern of change.

c. Make a prediction based upon patterns.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Can use graphing technology to plot a scatter diagram.
  • Can describe a relationship if one exists between points.
  • Can find a regression equation using graphing technology.
  • Can use the regression equation to make a prediction.
Teacher Vocabulary:
  • Regression Equation
  • "Best Fit"
  • Bivariate Data
  • Linear Pattern
  • Non-linear pattern
  • Scatter Plot
  • Quantitative Variable
  • Extrema
  • Inflection
Knowledge:
Students know:
  • how to plot points using graphing technology.
  • how to find a regression equation using graphing technology.
  • how to use a regression equation to make a prediction.
Skills:
Students are able to:
  • plot points.
  • Distinguish between linear and nonlinear functions.
  • Use graphing technology.
Understanding:
Students understand that:
  • Regression equations can be used to model data.
  • Graphing technology helps us find regression equations.
  • The regression equation can be used to make a prediction.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
MMOD.15.1: Define bivariate scatter plot, outlier, cluster, linear, nonlinear, positive and negative association, slope, intercept, linear, equation, concave up, concave down, and bivariate.
MMOD.15.2: Make a prediction based upon patterns.
MMOD.15.3: Describe patterns found in a scatter plot.
MMOD.15.4: Demonstrate how to label and plot information on a scatter plot (dot plot).
MMOD.15.5: Distinguish the difference between positive and negative correlation.
MMOD.15.6: When given data points, use technology to find the equation of a line.

Prior Knowledge Skills:
  • Define bivariate scatter plot, quantitative data, outlier, cluster, linear, nonlinear, and positive and negative association.
  • Describe patterns found in a scatter plot.
  • Demonstrate how to label and plot information on a scatter plot (dot plot).
  • Distinguish the difference between positive and negative correlation.
  • Recall how to describe the spread of the scatter plot (dot plot).
  • Create a scatter plot and line of best fit using data from a spreadsheet.
  • Organize and display bivariate quatitative data using a scatter plot, and extend from simple cases by hand to more complex cases involving a large data set using technology.
  • Create a scatter plot of data.
  • Calculate the fit of the function to the data by examining residuals.
Mathematics
MA2019 (2019)
Grade: 9-12
Precalculus
26. Graph functions expressed symbolically and show key features of the graph, by hand and using technology. Use the equation of functions to identify key features in order to generate a graph.

a. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

b. Graph trigonometric functions and their inverses, showing period, midline, amplitude, and phase shift.
Unpacked Content
Mathematics
MA2019 (2019)
Grade: 9-12
Precalculus
27. Compose functions. Extend to polynomial, trigonometric, radical, and rational functions.

Example: If T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.
Unpacked Content
Tags: asymptote, concavity, decreasing, differentiable, domain, extrema, function, increasing, inflection, mathematical modeling, point, precalculus, range, rational, relative
License Type: Custom Permission Type
See Terms: https://www.ck12info.org/terms-of-use/
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses
AccessibilityText Resources: Content is organized under headings and subheadings
Comments
  This resource provided by:  
Author: Hannah Bradley
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