The thermostat in an empty apartment is set to from 4:00 a.m. to 5:00 p.m. and to from 5:00 p.m. until 4:00 a.m. Here is a graph of the function that gives the temperature in degrees Fahrenheit in the apartment hours after midnight.
Graph of function plane, origin . Horizontal axis scale 0 to 22 by 2’s. Vertical axis scale 45 to 80 by 5’s. Function H starts at (0 comma 50) and is horizontal to (4 comma 50), then rises to (6 comma 65) and is horizontal to (17 comma 65). The function then drops to (19 comma 50) and is horizontal to (24 comma 50).
The owner of the apartment decides to change to a new schedule and sets the thermostat to change 3 hours later in the morning and the evening. On the same axes, sketch a graph of the new function, , giving the temperature as a function of time.
Explain what means in this context. Why is this a reasonable value for the function?
If , then what is the corresponding point on the graph of ? Use function notation to describe the point on the graph of .
A pumpkin pie recipe says to bake the pie at for 15 minutes, and then to adjust the temperature down to for 45 additional minutes. The function gives the oven temperature setting , in degrees Fahrenheit, minutes after the pie is placed in the oven.
Explain what means in this context.
Diego discovers that the temperature inside the oven is always 25 degrees warmer than the oven’s temperature setting. The function gives the actual temperature of Diego’s oven. If , then what is the corresponding point on the function ?
Write an expression for in terms of .
Problem 3
Here is the graph of for a function .
On the same axes, sketch a graph of .
On the same axes, sketch a graph of .
How do the graphs of and compare to ?
Graph of function f, no grid, origin O. Horizontal axis from negative 6 to 6 by 2's. Vertical axis from negative 10 to 10, by 2's. Function starts at negative 2 comma 8, curves downward and to the right passing through negative 2 comma 0, curves upwards around 2 comma negative 4, passes through 4 comma 2 and ends at 5 comma 8.
Problem 4
The graph shows the height of a tennis ball seconds after it has been hit.
Graph of a function, no grid, origin O.
Horizontal axis 0 to 3, by 1’s, labeled time, seconds. Vertical from 0 to 20, by 5’s, labeled height, feet. Function starts at 0 comma 5, curves upwards and to the right until 0 point 5 comma 12, then curves downwards until hitting the horizontal axis just after 1.
The function given by models the height of the ball in feet.
How high was the ball when it was hit? Where do you see this in the equation?
Suppose a second ball follows the same trajectory but is hit from 7 feet off the ground. Sketch the graph of the height of the second ball on the same axes.
Write an equation for a function that defines the height , in feet, of the second ball hit from 7 feet off the ground in terms of .
Describe a horizontal translation of the line to a line that contains the two labeled points.
Describe a vertical translation of the line to a line that contains the two labeled points.
Two points and graph of a line, origin O, with grid. Both axes from negative 6 to 4, by 2's. Line passes through negative 6 comma negative 4, 0 comma negative 1 and 4 comma 1. Points negative 4 comma 1 and negative 2 comma 2 plotted and labeled.
Does the function or the function fit the data better? Explain your reasoning.
Functions f and g and set of data on x y coordinate, no grid, origin o. 6 tick marks on horizontal axis, 4 tick marks on vertical axis. Function f, linear moving upwards and to the right, passing through 1 point. 12 points below, 2 points above line. Function g moving upwards and to the right, 11 points just below line, passes through 2 points, 2 points just above line.