9/8/2016 Created by Kenya Clo WARMUP 9/(# ππ πππππ π π πππππ βππ πππ’π π‘βπ ππ’ππππ ππ π‘πππ‘πππππ π ππππ ππ βππ ) GOING OVER THE GRAPHING WORKSHEETβ¦ Can you figure out the rules? 1) Input Output Garage g Baboon o Function o Kayak a Dinosaur u 3) Input Output = 2nd to last letter of input (the βpenultimateβ letter) 1 Denver 4 Jupiter 10 Zipper Friends Output Lischwe 2 Iowa 3 Pretzel 2 Mathematics 4 Equation Output Activity 2) Input 4) Input 5 Output Lime g Stop Sign r Basketball o 26 Sky b 6 Banana y Output = Place in alphabet of the first letter of the input Output = # of vowels in the input Output = First letter of the color of the input Table of Contents 9 Analyzing Key Features of Graphs p. 1 p. 2 p. 3 p. 4 p. 5 p. 6 p. 7 p. 8 p. 9 Consecutive Sums Project Stacking Cups Problem Converting Fractions and Decimals (1.1) Roots (1.8 & 1.9) Rational vs. Irrational (1.1) What is a Function? Function Notation Graphing Functions Analyzing Key Features of Graphs ONE IMPORTANT THING TO NOTICEβ¦ Did any of your graphs turn out to NOT BE FUNCTIONS? Objectives: -Compare linear/nonlinear equations -Describe important βkey featuresβ of graphs OKAY, NOW LOOK BACK AT YOUR FUNCTION GRAPHSβ¦ Look at the ones that are linear and the ones that are nonlinear Why do you think this happened??? What do you think made them linear or nonlinear? Come up with some conjectures. 1 9/8/2016 COPY: Letβs explore what the graphs of different functions look likeβ¦ Linear Equations Nonlinear Equations No exponent on the variable!!! Exponents other than 1 None of these other things: ο Variable inside a square roots Variable in a denominator https://www.desmos.com/calculator WHITEBOARDS! Today, you are NOT getting the regular whiteboards, you are getting the GRAPHING SHEETS. Variable inside an absolute value LINEAR OR NONLINEAR? π(π) = ππ + π Regular answers can go on the back. Graphs will go on the coordinate plane. Linear LINEAR OR NONLINEAR? LINEAR OR NONLINEAR? π(π) = ππ β π π π(π) = + π π Nonlinear Linear 2 9/8/2016 LINEAR OR NONLINEAR? π π(π) = β π π Nonlinear LINEAR OR NONLINEAR? LINEAR OR NONLINEAR? π(π) = ππ + ππ β π Nonlinear LINEAR OR NONLINEAR? π π = πππ β π π(π) = ππ β ππ Linear Linear LINEAR OR NONLINEAR? LINEAR OR NONLINEAR? π π π π =β π+ π π π(π) = π π β π Linear Nonlinear 3 9/8/2016 LINEAR OR NONLINEAR? LINEAR OR NONLINEAR? π π = ππ + ππ π(π) = π Nonlinear Linear LINEAR OR NONLINEAR? π(π) = ππ β π LINEAR OR NONLINEAR? π π β π = π(π) π Linear π Nonlinear LINEAR OR NONLINEAR? π π = πππ β π + π β π + Nonlinear π π LINEAR OR NONLINEAR? π = ππ + π Linear 4 9/8/2016 WHAT COULD BE SOME IMPORTANT THINGS ABOUT THIS GRAPH? KEY FEATURES OF GRAPHS Increasing: Where the y-values go up (from left to right) Decreasing: Where the y-values go down (from left to right) X-intercept: Where the graph crosses the x-axis Y-intercept: Where the graph crosses the y-axis Slope: How steep the graph is Increasing/Decreasing? KEY FEATURES? Both increasing Which graph has a greater x-intercept? Graph 1 Which graph has a greater y-intercept? Graph 1 Which graph has a greater slope? Graph 1 Graph 2 Graph 2 X-intercepts: -3 and 2 Y-intercept: -6 Increasing/Decreasing? First decreasing, then increasing KEY FEATURES? KEY FEATURES? Increasing/decreasing? Increasing/decreasing? Always increasing X-intercept? -8 Y-intercept? 6 Describe the slope. Increasing, then decreasing, then increasing, then decreasing, etc. X-intercept? βππ , βπ , π, π , ππ Y-intercept? π Describe the slope. The slope is not constant. The slope is not constant. Above and beyond answer: the slope starts out very steep, then gets gradually less steep 5 9/8/2016 KEY FEATURES? CHOOSE THE GRAPH THAT IS: Increasing/decreasing? Always increasing X-intercept? None Y-intercept? About 1.5 Decreasing, then increasing, then decreasing Has an x-intercept of 4 A B C Describe the slope. The slope is not constant. It starts not very steep, then gets steeper and steeper. DRAW A GRAPH WITH THE FOLLOWING CHARACTERISTICS: DRAW A GRAPH WITH THE FOLLOWING CHARACTERISTICS: x and y-intercepts are both zero Always increasing Always decreasing The slope changes Slope doesnβt change IS THIS POSSIBLE? WHICH OF THESE ARE POSSIBLE? Draw a graph that is increasing, where the x-and y-intercept are both 5. To connect these two points, A) A graph that is increasing only, which has an x-intercept of -4 and a y-intercept of 6. the graph must decrease! B) A graph that is increasing, then decreasing, has xintercepts of 5 and -5, and a y-intercept of -9. C) A graph that is increasing, then decreasing, then increasing again, that has x-intercepts of -8, 2, and 7, and a y-intercept of 4. IMPOSSIBLE 6 9/8/2016 HOMEWORK Key Features Half-Sheet 7
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