Getting Information From Graphs

Table of Contents 46: Warm-Up 47: How Do I Interpret Movement in Visual Representations of Data?

Warm Up 1a. How do you know if a function is increasing? 1b. Give a real life example of an increasing function 2a. How do you know if a function is decreasing? 2b. Give a real life example of a decreasing function

Learning Intention/Success Criteria LI: We are learning how to interpret movement in visual representations of data SC: I know how to -recognize input and output values based on axis labels -recognize and interpret x- and y-intercepts -interpret different shapes of a graph in context -interpret the meaning of increasing, decreasing, and constant in context

EQ: How Do I Interpret Movement in Visual Representations of Data? 12/4/2018

Maximum The highest point in a graph Minimum The lowest point in a graph Where the line crosses the x-axis X-Intercept The contextual meaning changes based on the label Y-Intercept Where the line crosses the y-axis The contextual meaning changes based on the label

Increasing Function A function a positive slope The steeper the line, the faster the movement Decreasing Function A function with a negative slope The steeper the line, the faster the movement

Constant Function A function with zero slope The context will change based on the labels

Example 1: Show on the graph where the function is increasing, decreasing, or constant 2 3 1 5 4 Increasing Decreasing Constant

Guided Practice 1 Show on the graph where the function is constant, increasing, or decreasing Constant Increasing Decreasing 4 2 3 5 8 1 7 6

Example 2: Show on the graph where the function is constant, increasing, or decreasing 4 3 1 2 5 Constant Increasing Decreasing

Guided Practice 2 Show on the graph where the function is constant, increasing, or decreasing 5 3 Constant Increasing Decreasing 1 4 2

Constant Increasing Decreasing Example 3: Cierra goes for a ride on her skateboard on a straight and level street. She starts at home and travels up and back. This is a graph of her distance from home versus time. 6 5 7 2 3 1 4 Constant Increasing Decreasing

What was Cierra doing between times B and C? Cierra was not moving. Her distance from home was constant as time increased.

During which times was Cierra traveling away from her house? Explain. Cierra traveled away from home in Points A to B (1) and Points E to F (5) When the graph increased, it showed that Cierra traveled away from her house.

During which times was Cierra going fastest on her skateboard? Cierra traveled the fastest between Points E to F (5) A to B (1) : B to C (2): C to D (3): D to E (4): E to F (5): F to G (6): G to H (7): 4/2 -1 4 -7/2

What was Cierra doing between points G and H? Explain. Cierra was traveling straight home This decreasing line shows that she is going back home, without stopping.

Example 4: Keoni walks at a constant rate and arrives 10 minutes before the bus arrives. Distance from home time

Guided Practice 3 - 7 Keoni is late. He runs as fast as he can until he gets tired, and then walks the rest of the way, arriving just in time to catch the bus. Distance from home time

Keoni walks at a constant rate until he runs into one of his old acquaintances, one with whom he used to get into trouble with all the time. This acquaintance is skipping school today and is trying to convince Keoni to join her. Keoni talks with her for about 5 minutes, realizes he will miss the bus if he doesn’t leave right away and runs the rest of the way at a constant rate, arriving just in time to be the last one on the bus Distance from home time

This time Keoni is really late This time Keoni is really late! He runs as fast as he can all the way to the bus stop, but runs slower and slower as he gets tired…after all it is a whole mile. But, he appears to have missed the bus. He waits and waits (about 20 minutes) and then remembers it is Prince Kuhio Day…a holiday!! He runs as fast as he can home…exactly the same as on the way to the bus stop…fast at first and tiring when he approaches his destination…just in time to catch the end of the morning cartoons Distance from home time

Keoni is early today, so he walks at a leisurely rate Keoni is early today, so he walks at a leisurely rate. About a quarter of the way to school, he realizes he forgot his math homework, again! He walks briskly back home, but about halfway back home, he remembers he didn’t have math homework, so he walks even faster to the bus stop, arriving about 1 minute before the bus arrives. Distance from home time

Keoni has plenty of time to get to the bus Keoni has plenty of time to get to the bus. He walks slowly for awhile, but then stops to watch a gecko chase a bug. He continues at a slightly faster pace for awhile longer and stops again, this time to tie his shoe and watch a man unload tools from his truck. He realizes he’s possibly late now and continues at a still faster pace until he arrives just in time to catch the bus. Distance from home time