Activity 6 interpreting graphs of functions answers

By now, students have had multiple opportunities to interpret graphs of functions and to create them (primarily by plotting known input-output pairs of a function or by using descriptions of the situation). Students have also acquired essential vocabulary to communicate about graphs of functions, and used average rate of change as a way to measure how a function changes.

In this lesson, students apply these insights and skills to interpret or create graphs of functions that are less well defined and that model real-life situations that are more complex. The lesson includes two main activities about flag-raising and two optional activities that use other contexts.

Information about the functions is presented in the form of verbal descriptions, video clips, and images. More ambiguity is involved here than in cases students have previously encountered, so they will need to persevere in sense making and problem solving (MP1). At times, the information given may be inadequate, so students will need to make assumptions and decisions in order to produce graphs that show the desired behaviors or meet certain requirements. Along the way, students engage in important aspects of mathematical modeling (MP4).

MATH TERMSLesson 6-1Key Features of GraphsActivity 6• Interpreting Graphs of Functions83continuedACTIVITY 6

My Notes© 2014 College Board. All rights reserved.11.The graph below shows five points that make up the functionh. Is thefunctionhcontinuous? Explain.4321-1-2-3-5-4yx146532-3-1-212.A function has three relative maximums:-2, 10.3, and 28. One of therelative maximums is also the absolute maximum. What is theabsolute maximum?Tell whether each statement is sometimes, always, or never true. Explainyour answers.13.A relative minimum is also an absolute minimum.14.An absolute minimum is also a relative minimum.Tom hiked along a circular trail known as the Juniper Loop. The graph showshis distancedfrom the starting point aftertminutes.Check Your UnderstandingTime (minutes)Distance from Start (km)603090246813579dt12015015.Identify the domain and range of the function shown in the graph.16.Identify the absolute minimum of the function. What does it represent?Lesson 6-1Key Features of Graphs84SpringBoard®MathematicsAlgebra 1, Unit 2• FunctionscontinuedACTIVITY 6

My Notes© 2014 College Board. All rights reserved.17.In this function, the absolute minimum corresponds to two points onthe graph. What are the two points? What do they represent in thiscontext?18.Identify the absolute maximum of the function. What does it represent?19.What points on the graph correspond to the absolute maximum? Whatdoes this mean in the context of Tom’s hike?20.Identify any relative minimums for the function shown in the graph.21.Identify any relative maximums for the function shown in the graph.22.What are the independent and dependent variables for the functionrepresenting Tom’s hike?23.Explain how to determine the maximum and minimum values of afunction by examining its graph.24.Is it possible for a function to have more than one absolute maximumor absolute minimum value? Explain.Check Your UnderstandingLesson 6-1Key Features of GraphsActivity 6• Interpreting Graphs of Functions85continuedACTIVITY 6

My Notes© 2014 College Board. All rights reserved.LESSON 6-1 PRACTICEModel with mathematics.Use the graph below for Items 25–30.123456Minutes Since Bath BeganBath Water DepthdtDepth of Bath Water (in.)789 10 11 12 13-1-2-31023456789101125.What are the independent and dependent variables? Explain.26.Use set notation to write the domain and range of the function.27.Is the function discrete or continuous? Explain.28.What is they-intercept? Interpret the meaning of they-intercept inthisuni00A0context.29.Identify any relative maximums or minimums of the function.30.Identify the absolute maximum and absolute minimum values.Interpretuni00A0their meanings in this context.Lesson 6-1Key Features of Graphs86SpringBoard®MathematicsAlgebra 1, Unit 2• FunctionscontinuedACTIVITY 6

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Professor

Carolyn Jonas- Morrison