Section 5.3:
Interpreting and Sketching Graphs
Certain Properties of Graphs provide much information about a given situation.
A)
general shape
B)
scale
C)
starting point (y-intercept)
D)
ending point
General Shape
Linear
-the change in the independent and dependent
variables is constant
- horizontal line - the y-value is constant
-diagonal line slanting up to the right: As
the x-value increases so does the y-value.
-diagonal line slanting down to the left: As
the x-value increases the y-value decreases.
-y-intercept: it gives the value of the dependent
variable (y) when the independent variable (x)
is zero.
Non-Linear
- the change in the independent and
dependent variable is not constant
Discrete Data: Data values on a graph that are not connected. This graph can only show points
because the values in between them have no meaning. (An infinite number of points exist
between any two other values.)
Continuous Data: Data values on a graph that are connected. The values between points have
meaning. (A finite number of points exist between any two other values.)
Examples
1.
Water was taken out of a tap and a thermometer was inserted into it.
Continuous Graph
a) What was the starting temperature of the water?
b) What was the temperature of the water after 18 minutes?
c) When was the temperature of the water 40o ?
d) When was the temperature of the water constant?
e) When was the temperature increasing?
f) When was the temperature decreasing?
g) What was the final temperature of the water?
h) Name the dependent variable.
i) Name the independent variable.
2.
The data represents the height of a newly planted tree in Mr. Hunt's yard.
Discrete graph
a) How tall was the tree when it was first bought?
b) How tall was the tree after 4 weeks?
c) After how many weeks was the tree 70 cm tall?
d) When did the tree get the least amount of water/sunlight?
e) When did the tree get the most amount of water/sunlight?
f) What is the domain of the graph?
g) What is the range of the graph?
h) Name the dependent variable.
i) Name the independent variable.
3.
The graph shows the distance a rock climber is from the base of a cliff as time passes.
Using the words climbing, resting, or descending, describe what the climber is doing
during each segment shown. Explain your choice.
For any section that you listed as “climbing,” how would you change the graph to show that the
person is climbing faster?
What would you add to the graph to show the climber’s return to the bottom of the cliff?
4.
This graph represents a day trip from Gambo to Grand Falls - Windsor, a distance of
approximately 140 km. Describe the journey for each segment of the graph.
5.
Match each graph with a situation from the list. Explain your choice. Suggest titles for
each axis to show the quantities being compared.
a) the temperature of a cup of hot chocolate over time
b) a car accelerating to a constant speed
c) the distance a person walks during a hike
d) the height of a soccer ball kicked across a field
6.
Describe the motion of the object.
7.
In 2010, Jamaican track and field superstar, Usain Bolt, set a world record in the 100 m
race, finishing in 9.58 s. Sketch a possible distance versus time graph to best represent his
race.
8.
A salmon is swimming upstream. For the first hour, it swims strongly and at a constant
speed. For the next two hours, due to fatigue and a stronger current, it swims half as fast.
It finally realizes it has passed its destination so, for the final half-hour, it stops
swimming and allows the current to carry it slowly back downstream. Sketch a possible
speed versus time graph to best represent the path of the salmon.
Summary
1.
For a graph of distance as a function of time, what does each segment represent?
■ a horizontal line segment
■ a segment that goes up to the right
■ a segment that goes down to the right
2.
For a graph of speed as a function of time, what does each segment represent?
■ a horizontal line segment
■ a segment that goes up to the right
■ a segment that goes down to the right