NAME DATE PERIOD. Study Guide and Intervention. Parent Functions and Transformations. Name Characteristics Parent Function

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1 -7 Stud Guide and Intervention Parent Graphs The parent graph, which is the graph of the parent function, is the simplest of the graphs in a famil. Each graph in a famil of graphs has similar characteristics. Name Characteristics Parent Function Constant Function Straight horizontal line = a, where a is a real number Linear Function Straight diagonal line Identif Function = Absolute Value Function Diagonal lines shaped like a V = Quadratic Function Curved like a parabola = a. Eample Identif the tpe of function represented b each graph. b. Lesson -7 The graph is a diagonal line. The graph represents a linear function. The graph is a parabolic curve. The graph represents a quadratic function. Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Eercises Identif the tpe of function represented b each graph Chapter 3 Glencoe Algebra

2 -7 Stud Guide and Intervention (continued) Transformations Transformations of a parent graph ma appear in a different location, ma flip over an ais, or ma appear to have been stretched or compressed. Eample Describe the reflection in = -. Then graph the function. The graph of =- is a reflection of the graph of = in the -ais = = Eercises Describe the translation in each function. Then graph the function. 1. = -. = + 3. = - 3 Describe the dilation in each function. Then graph the function.. =. = 1 6. = Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter Glencoe Algebra

3 -7 Skills Practice Parent Functions and Transformation Identif the tpe of function represented b each graph. 1.. Describe the translation in each equation. Then graph the function. 3. = -. = ( + 1) Lesson -7 Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Describe the reflection in each equation. Then graph the function.. = - 6. = - 7. Biolog A biologist plotted the data from his latest eperiment and found that the graph of his data looked like this graph. What tpe of function relates the variables in the eperiment? Chapter Glencoe Algebra

4 -7 Practice Describe the translation in each function. Then graph the function. 1. = + 3. = - 3 Describe the reflection in each function. Then graph the function. 3. = (-). = -(3) Describe the dilation in each function. Then graph the function.. = 6. = 7. CHEMISTRY A scientist tested how fast a chemical reaction occurred at different temperatures. The data made this graph. What tpe of function shows the relation of temperature and speed of the chemical reaction? Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. -1 Chapter 6 Glencoe Algebra

5 -7 Word Problem Practice 1. GAMES Pedro decided to measure how close to a target he and his friends could throw a football. The counted 1 point for each foot awa from the target that the football landed. The graph of points versus distance thrown is shown here. What tpe of function had Pedro and his friends followed? BUSINESS Maria earns an hourl wage of $1. She drew the following graph to show the relation of her income as a function of the hours she works. How did she modif the identit function to create her graph? Net Salar ($) Hours Worked Lesson -7 Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. ASTRONOMY The graph shows the velocit of the space probe Cassini as it passed Saturn. What tpe of function best models Cassini s velocit? Velocit (miles per hour) 3. GEOMETRY Chen made this graph to show how the perimeter of a square changes as the length of one side is increased. The original graph showed an identit function. How has it been dilated? Perimeter 7,,, Time (seconds). HOBBIES Laura launched a model rocket into the air. The height of her rocket over time is shown b the graph. Height (meters) Time (seconds) a. What tpe of function does the graph show? b. In which ais has the function been reflected? c. Which directions has the graph been translated? How man units? 1 3 Side Length d. What is the equation for the curve shown on the graph? Chapter 7 Glencoe Algebra

6 -7 Enrichment Parent Graphs and Relationships An additional famil of graphs has the parent function = 3. The parent graph of this famil of graphs is shown below. O One leg of this graph (the region in Quadrant 3) points downwards. The other leg (the region in Quadrant 1) points upwards. This function can be transformed in the same wa as other functions. For instance, multipling b -1 reflects the function in the -ais. 1. Describe the translation in = 3 +. Then graph the function. O. Describe the reflection in - = 3. Then graph the function. O 3. Describe the dilation in = 1 3. Then graph the function. O Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 8 Glencoe Algebra

7 -7 Graphing Calculator Activit Transformations: Cube Function A graphing calculator can be used to displa transformations to the cube function. This is done b using the ke followed b 3 to raise to the 3rd power. Eample Graph f() = 3-1. Evaluate the function for =., = 1, = 1., =, = -.7, and = -1.. Enter f() in Y1. Graph the function. Kestrokes: Y= 3 1 ZOOM 6 Lesson -7 [-1, 1] scl:1 b [-1, 1] scl:1 Use TRACE to evaluate each function for the given values. Kestrokes: TRACE. ENTER 1 ENTER 1. ENTER ENTER ( ).7 ENTER ( ) 1. ENTER f(.) = -.36, f(1) =, f(1.) =.37, f() = 7, f(-.7) = -1.33, f(-1.) = -.78 Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Eercises Graph each function. Evaluate the function for = 1, = 1., and = g() = 3 +. g() = ( + ) 3 3. g() = ( - 1) 3. g() = - 3. g() = (-) 3 6. g() = 3 Chapter 9 Glencoe Algebra