ALEX Classroom Resources

   View Standards     Standard(s): [MA2019] MOD-19 (9-12) 15 :

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.

This informational material will explain how to describe the relationship between two variables as either concavity or inflection using functions and graphical representations:

• • When the sign is negative, the curve is concave down.
  • When the sign is positive, the curve is concave up.

There is a corresponding video available. Practice questions with a PDF answer key are provided.

   View Standards     Standard(s): [MA2019] MOD-19 (9-12) 15 :

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.

This video will explain how to solve functions to determine if the relationship between the variables shows concavity or inflection.

   View Standards     Standard(s): [MA2019] MOD-19 (9-12) 15 :

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.

This self-checking online assessment has 10 questions that will help students practice solving functions to determine if the relationship between the variables shows concavity or inflection. There are hints available on the screen, and there is an online scratchpad that students can use to work on the problems.

   View Standards     Standard(s): [MA2019] MOD-19 (9-12) 15 :

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.

This self-checking online assessment has 10 questions that will help students practice solving problems to identify and describe the relationship between variables as extrema. There are hints available on the screen, and there is an online scratchpad that students can use to work on the problems.

   View Standards     Standard(s): [MA2019] MOD-19 (9-12) 15 :

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.

[MA2019] PRE-19 (9-12) 26 :

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.

[MA2019] PRE-19 (9-12) 27 :

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.

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.