SECTION 1 8 INTERPRETING GRAPHS OF FUNCTIONS ALGEBRA

SECTION 1. 8 INTERPRETING GRAPHS OF FUNCTIONS ALGEBRA 1

WELCOME BACK! WARM- UP AGENDA CREATE THE GRAPH FOR EACH SITUATION IN RELATION TO TIME: • PASS BACK QUIZZES 1. THE HEIGHT OF A BALL AS A BASEBALL PLAYER THROWS IT AS HIGH AS HE CAN INTO THE AIR AND THEN HITS THE GROUND. • HOMEWORK TIME 2. THE SPEED OF A CAR AS IT GETS OFF THE HIGH WAY, STOPS AT A STOP LIGHT, AND THEN CONTINUES TO DRIVE THROUGH SIDE STREETS. • 1. 8 INTERPRETING GRAPHS

OBJECTIVES • INTERPRET THE CONTEXT OF A GRAPH OF FUNCTIONS • CREATE A GRAPH WITH GIVEN SPECIFIC CONDITIONS

LINEARITY & INTERCEPTS • LINEAR: THE GRAPH OF THE FUNCTION IS A STRAIGHT LINE • NON-LINEAR: THE GRAPH OF THE FUNCTION IS NOT A STRAIGHT LINE

LINEARITY & INTERCEPTS X- Intercept • INTERCEPTS: POINTS ON THE GRAPH THAT YIntercept INTERSECT AN AXIS.

LINEARITY & INTERCEPTS • NONLINEAR

LINE SYMMETRY CAN YOU DRAW THE OTHER HALF OF THE IMAGE?

LINE SYMMETRY A GRAPH HAS LINE SYMMETRY IN SOME VERTICAL LINE IF ONE HALF IS A MIRROR IMAGE OF THE OTHER. THIS GRAPH HAS LINE SYMMETRY AT X = 2.

LINE SYMMETRY EXAMPLE 1: LET THE GRAPH REPRESENT AN OBJECT BEING LAUNCHED INTO THE AIR. WHAT DOES THE SYMMETRY OF THE GRAPH MEAN IN THIS CONTEXT? IT TOOK THE SAME AMOUNT OF TIME TO GO UP AS IT DID DOWN

POSITIVE & NEGATIVE • POSITIVE: WHEN THE FUNCTION’S GRAPH IS ABOVE THE X-AXIS. • NEGATIVE: WHEN THE FUNCTION’S GRAPH IS BELOW THE X-AXIS.

INCREASING & DECREASING • INCREASING: THE GRAPH MOVES UP • DECREASING: THE GRAPH MOVES DOWN

END BEHAVIOR AS X-VALUES INCREASE, Y-VALUES INCREASE • DESCRIBES THE VALUES OF A FUNCTION AS XVALUES BECOME VERY SMALL AND VERY LARGE AS X-VALUES DECREASE, Y-VALUES DECREASE

EXTREMA • EXTREMA: HIGH OR LOW FUNCTION VALUES • RELATIVE MINIMUM: NO OTHER POINTS NEARBY HAVE A LESSER YCOORDINATE • RELATIVE MAXIMUM: NO OTHER POINTS NEARBY HAVE A GREATER Y-

COMPREHENSIVE EXAMPLE • U. S. RETAIL SALES OF VIDEO GAMES FROM 2000 -2009 CAN BE MODELED BY THE FUNCTION AT THE RIGHT. • A) ESTIMATE AND INTERPRET WHERE THE FUNCTION IS POSITIVE AND NEGATIVE

COMPREHENSIVE EXAMPLE • B) ESTIMATE AND INTERPRET WHERE THE GRAPH IS INCREASING AND DECREASING.

COMPREHENSIVE EXAMPLE • C) ESTIMATE AND INTERPRET WHERE THE GRAPH HAS RELATIVE EXTREMA

COMPREHENSIVE EXAMPLE • D) ESTIMATE AND INTERPRET THE INTERCEPTS OF THE GRAPH

AS X INCREASES, Y DECREASES COMPREHENSIVE EXAMPLE • E) ESTIMATE AND AS X DECREASES, Y INTERPRET THE END DECREASES BEHAVIOR OF THE GRAPH THE MODEL INDICATES THERE WERE NEGATIVE SALES PRIOR 2000 AND AFTER 2009.

SKETCHING A GRAPH •

EXIT SLIP • PLEASE COMPLETE THE EXIT SLIP ON YOUR OWN AND PLACE IT IN THE BINS ON THE CABINET DOOR. BE HONEST WITH YOURSELF AND PUT IT IN THE APPROPRIATE BIN. HOMEWORK • 1. 8 PRACTICE WORKSHEET ALL