Here are four equations of absolute value functions and three coordinate pairs. Each coordinate pair represents the vertex of the graph of an absolute value function.

Match the equation of each function with the coordinates of the vertex of its graph. The vertex coordinates of the graph of one equation are not shown.

Function is defined by the equation .

Function is defined by the equation .

Describe how the graph of function relates to the graph of , or sketch the graphs of the two functions to show their relationship.

The temperature was recorded at several times during the day. Function gives the temperature in degrees Fahrenheit, hours since midnight. Here is a graph for this function.

1. Pick two consecutive points, and connect them with a line segment.

   Estimate the slope of that line. Explain what that estimated value means in this situation.

   

   Discrete graph of temperature over time, coordinate plane, origin O. Horizontal axis scale 0 to 25 by 5’s, labeled “time of day”. Vertical axis scale 30 to 70 by 10’s, labeled “temperature (Fahrenheit)”. The points are near (1 comma 42), (2 comma 40), (3 comma 39), (4 comma 38), (5 comma 36), (6 comma 36), (7 comma 37), (8 comma 41), (9 comma 47), (10 comma 51), (11 comma 55), (12 comma 61), (13 comma 64), (14 comma 66), (15 comma 68), (16 comma 69), ( 17 comma 69 point 3), (18 comma 69), (19 comma 66), (20 comma 63), (21 comma 57), (22 comma 50), (23 comma 41) and (24 comma 32).

2. Pick two nonconsecutive points, and connect them with a line segment. Estimate the slope of that line. Explain what that estimated value means in this situation.

A tennis ball is dropped from an initial height of 30 feet. It bounces 5 times, with each bounce height being about of the height of the previous bounce.

Sketch a graph that models the height of the ball over time. Be sure to label the axes.