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Transforming Linear Functions – Teacher NotesActivity OverviewIn this activity you will determine the transformations of linear functions you get by changing m & b in the function: f(x)=mx+bSend the file transforming linear function.tns to all student calculators. Open TI-Nspire document transforming linear functions.tns Use /? to move from page to page Move to page 1.2Graph the function f(x) = xStudents will sketch a graph of the parent functionPress /T to split the screen and show the table for the functionStudents will complete the table for the parent function – include 2 negative, 2 positive and zero for the x valuesNote: Discuss with students what a parent function is -the most basic of a specific family of functions. This is the parent function of linear functions. The transformations we will discuss will all be compared to the parent function.Sketch the graph and complete the table.-5334023622000 xf1(x)Move to page 1.33916045-254000 Graph the functions f1(x) = x and f2(x) = -xCompare and contrast f(x)=x and f(x)=-xStudents will sketch the graph with both lines – label the graph and complete the tableStudents will discuss that happened when the slope went from 1 to -1Develop the concept of a reflection over the x-axis (some will say it is over the y-axis, but in other function families the leading negative is a reflection over the x, so be sure they say it is a reflection over the x-axis)To prove their conjecture is correct, have students graph (on the same graph, f(x)=2x and f(x) = -2x or some other combination of two functions that are a reflection of the otherxf1(x)f2(x)Move to page 1.4Complete the statement for the transformation when m<0In a linear function, if m < 0 the function has a reflection across the x – axis.Move to page 2.1Using the slider on the next page, what happens to the graph (compare it to the parent function) when m is changed?Move to page 2.2Note: have students discuss what is happening to the graph when m is changed using the slider. Guide students to develop the rule for the transformation when m>1 and when 0<m<1.Move to page 2.3 Complete the statements on the pageAnswers for both - verticalMove to page 3.1Move to page 3.2 Using the slider, what happens to the graph (compared to the parent function) when b is changed? Move to page 3.3 Complete the statement on page 3.3 for the transformation when b changesIn a linear function, if |b|>0, the function has a vertical translationMove to page 4.1Move to page 4.2.Using the sliders, what happens to the graph (compared to the parent function) when m & b are changed? Move to page 4.3 Does one changing one change the other?In what order should transformations be listed?Move to page 5.1 – can be sent as quick pollsPage 5.2Answer: vertical stretch by a factor of 3, vertical translation up 1 unitPage 5.3Answer: reflection over the x-axis, vertical shrink by a factor of 23 , vertical translation up 4 unitsPage 5.4Answer: reflection over the x-axis, vertical stretch by a factor of 2, vertical translation down 3 unitsMove to page 6.1 (or can use additional .tns file named “transforming linear functions Student Activity last question” )Answers:Vertical stretch by a factor of 2, vertical translation down 5 unitsVertical shrink by a factor of 13, vertical translation up 2 unitsReflection over the x-axis, vertical stretch by a factor of 3, vertical translation down 1 unitVertical translation down 23 unitsNote: when m is one, students tend to put vertical stretch by a factor of 1, you will need to help them realize that when m is 1, it is the same as the parent function so there is not transformation of m.Created by Sherri PhegleyFort Settlement Middle SchoolFort Bend ISDSheryl.phegley@fortbend.k12.tx.us ................
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