A.4.6.3 The Jump
- Author:
- LeonMilewski
In a bungee jump, the height of the jumper is a function of time since the jump begins.
Function h defines the height, in meters, of a jumper above a river, t seconds since leaving the platform.
Here is a graph of function h, followed by five expressions or equations and five graphical features.
Expression/Equations:
h(0)
h(t)=0
h(4)
h(t)=80
h(t)=45
Features:
first dip in the graph
vertical intercept
first peak in the graph
horizontal intercept
maximum
1. Match each description about the jump to a corresponding expression or equation and to a feature on the graph.
One expression or equation does not have a matching verbal description. Its corresponding graphical feature is also not shown on the graph. Interpret that expression or equation in terms of the jump and in terms of the graph of the function. Record your interpretation in the last row of the table.
Expression/Equations:
h(0)
h(t)=0
h(4)
h(t)=80
h(t)=45
Features:
first dip in the graph
vertical intercept
first peak in the graph
horizontal intercept
maximum
1. Match each description about the jump to a corresponding expression or equation and to a feature on the graph.
One expression or equation does not have a matching verbal description. Its corresponding graphical feature is also not shown on the graph. Interpret that expression or equation in terms of the jump and in terms of the graph of the function. Record your interpretation in the last row of the table.2. Use the graph to: a. estimate h(0) and h(4) b. estimate the solutions to h(t)=45 and h(t)=0
Keep students in groups of 2. Display the graph and the descriptions of two functions for all students to see:
- Function b gives the vertical distance (or the height) of a bee from the ground as a function of time, t.
- Function d gives the distance of a child from where his mom is sitting as a function of time, t.
- vertical intercept
- horizontal intercept
- maximum
- minimum
- intervals where the function is increasing
- intervals where the function is decreasing
- intervals where the function is staying constant
- solution or solutions to b(t)=3.5 or d(t)=3.5
- “How can you tell that a point on the graph is a maximum, a minimum, or neither?” (Look around it, left and right, to see whether the given point is higher than all the other points, lower than all the others, or neither.)
- “How many intercepts can the graph of a function have?” (An unlimited number on the horizontal axis, but only one on the vertical axis.)