7.3 Matching Up Investigation
Name: ___________________________
First, you’ll consider the concept of increasing and decreasing functions.
STEP 1 These are graphs of increasing functions.
What do they have in common?
How would you describe the rate of change in each? Is the rate increasing at a constant rate? If not, is the
rate getting smaller or larger as x gets larger? Or is the rate of change constant for a while, and then change
to a new constant rate, and then change again …?
Graph A
Graph B
Graph C
Rates of change
for each graph
STEP 2 These are graphs of decreasing functions.
What do they have in common? How are they different from those in Step 1?
How would you describe the rate of change in these graphs?
Graph D
Graph E
Graph F
Rates of change
for each graph
Group Check: _____
_____
_____
In Steps 3 to 5, you’ll use this vocabulary to find and describe the graph that
matches each of these real-world situatations. Two of the graphs will not be
used.
Situation A During the first few years, the number of deer on the island
increased by a steady percentage. As food became less plentiful, the growth
rate started slowing down. Now, the number of births and deaths is about
the same.
Step 3 In Situation A decide which quantities are varying. Also decide
which variable is independent and which is dependent.
What quantities vary?____________________________
Independent Variable: ___________ Dependent Variable: _____________
Step 4
Match the graph that best fits the situation. Label the axes on the
graph.Write a description of the function and its graph using
words such as linear, nonlinear, increasing, decreasing, rate of
change, maximum or greatest value, or minimum or least value.
Matching Graph: _____
Description of Function and its Graph:
Step 5: Situation B
In the Northern Hemisphere the amount of daylight increases slowly from
January through February, faster until mid-May, and then slowly until the
maximum in June. Then it decreases slowly through July, faster from
August until mid-November, and then slowly until the year’s end.
What quantities vary?____________________________
Independent Variable: ___________ Dependent Variable: _____________
Match the graph that best fits the situation. Label the axes on the graph.
Write a description of the function and its graph using words such as linear,
nonlinear, increasing, decreasing, rate of change, maximum or greatest
value, or minimum or least value.
Matching Graph: _____
Description of Function and its Graph:
.
Group Check: _____
_____
_____
Step 6: Situation C
If you have a fixed amount of fencing, the width of your rectangular garden
determines its area. If the width is very short, the garden won’t have much
area. As the width increases, the area also increases. The area increases
more slowly until it reaches a maximum. As the width continues to
increase, the area becomes smaller more quickly until it is zero.
What quantities vary?____________________________
Independent Variable: ___________ Dependent Variable: _____________
Match the graph that best fits the situation. Label the axes on the graph.
Write a description of the function and its graph using words such as linear,
nonlinear, increasing, decreasing, rate of change, maximum or greatest
value, or minimum or least value.
Matching Graph: _____
Description of Function and its Graph:
Step 7: Situation D
Your cup of tea is very hot. The difference between the tea temperature and the
room temperature decreases quickly at first as the tea starts to cool to room
temperature. But when the two temperatures are close together, the cooling rate
slows down. It actually takes a long time for the tea to finally reach room
temperature.
What quantities vary?____________________________
Independent Variable: ___________ Dependent Variable: _____________
Match the graph that best fits the situation. Label the axes on the graph.
Write a description of the function and its graph using words such as linear,
nonlinear, increasing, decreasing, rate of change, maximum or greatest
value, or minimum or least value.
Matching Graph: _____
Description of Function and its Graph:
Group Check: _____
_____
_____
Step 8: Increasing/Decreasing, Linear/Nonlinear
Use the intervals marked on the x-axis to help you discuss where the function is increasing or decreasing and where it
is linear or nonlinear.
Word Bank (words can be used more than once): increasing, decreasing, linear, and nonlinear
On the interval0 ≤ 𝑥 ≤ 3.0, the function is _________________ and _________________. As 𝑥 increases steadily, 𝑦
changes at a varying rate, so the graph is _____________________. When read from left to right, the graph rises. So
the y-values grow and the function is ________________________.
On the interval3.0 ≤ 𝑥 ≤ 4.0, the function appears ________________ and is _________________. Because 𝑦
appears to change at a constant rate on the graph, the function is _______________. So the y-values drop and the
function is ______________________.
Step 9: Continuous and Discrete Functions
In your own words…
What is a continuous function?
What is a discrete function?
Homework: Finish 7.3 WS & 7.3 pg. 408 #2-6, 8, 11, 13, 15-16