M
Math Coach Amy
Amy Ferguson Moncure

Algebra 1 · Unit 2

Discrete or Continuous

Decide whether a graph or a situation is discrete or continuous.

Jump to section:

Key Ideas Easy · Graphs Medium · Situations Hard · Graph or Situation
What to Remember

Discrete

A discrete graph is separate points. Nothing is drawn between the dots.

A count of whole objects is discrete: people, tickets, messages, pizzas.

Continuous

A continuous graph is connected. A line, a ray, a segment, and a curve are continuous.

An arrow means the graph keeps going. The values between the points you see are included.

Time, distance, temperature, and weight can fall between whole numbers. Those situations are continuous.

Graph or story

If a graph is shown, use the graph. Separate points are discrete even when the story is about time or distance.

Easy

Graphs

Dots are discrete. A connected line or curve is continuous.

Example
Is this graph discrete or continuous?
−5−4−3−2−112345−5−4−3−2−112345xy

Separate points → discrete. A connected line or curve → continuous.

The graph shows separate points.

Nothing is drawn between the points.

Discrete.

Answer: Discrete

1
Is this graph discrete or continuous?
−5−4−3−2−112345−5−4−3−2−112345xy
Show Answer

Separate points → discrete. A connected line or curve → continuous.

The graph is connected.

The values between the points you see are included.

Continuous.

Answer: Continuous

2
Is this graph discrete or continuous?
−5−4−3−2−112345−5−4−3−2−112345xy
Show Answer

Separate points → discrete. A connected line or curve → continuous.

The graph shows separate points.

Nothing is drawn between the points.

Discrete.

Answer: Discrete

3
Is this graph discrete or continuous?
−5−4−3−2−112345−5−4−3−2−112345xy
Show Answer

Separate points → discrete. A connected line or curve → continuous.

The graph is connected.

The values between the points you see are included.

Continuous.

Answer: Continuous

4
Is this graph discrete or continuous?
−5−4−3−2−112345−5−4−3−2−112345xy
Show Answer

Separate points → discrete. A connected line or curve → continuous.

The graph is connected.

The values between the points you see are included.

Continuous.

Answer: Continuous

5
Is this graph discrete or continuous?
−5−4−3−2−112345−5−4−3−2−112345xy
Show Answer

Separate points → discrete. A connected line or curve → continuous.

The graph shows separate points.

Nothing is drawn between the points.

Discrete.

Answer: Discrete

Medium

Situations

Decide from the story. No graph is given.

Example
The number of tickets sold at a concert.

A count of whole objects is discrete. A measurement that can fall between whole numbers is continuous.

You count tickets. The number of tickets is a count of whole objects.

Discrete.

Answer: Discrete

1
The temperature in a classroom from morning to afternoon.
Show Answer

A count of whole objects is discrete. A measurement that can fall between whole numbers is continuous.

Temperature can fall between whole numbers, such as 70.4 degrees.

Continuous.

Answer: Continuous

2
The number of students in a club.
Show Answer

A count of whole objects is discrete. A measurement that can fall between whole numbers is continuous.

You count students. That is a count of whole objects.

Discrete.

Answer: Discrete

3
The distance a bike travels during a ride.
Show Answer

A count of whole objects is discrete. A measurement that can fall between whole numbers is continuous.

Distance can fall between whole numbers, such as 3.2 miles.

Continuous.

Answer: Continuous

4
The number of text messages sent in a day.
Show Answer

A count of whole objects is discrete. A measurement that can fall between whole numbers is continuous.

You count messages. That is a count of whole objects.

Discrete.

Answer: Discrete

5
The weight of grapes in a bag.
Show Answer

A count of whole objects is discrete. A measurement that can fall between whole numbers is continuous.

Weight can fall between whole numbers, such as 2.5 pounds.

Continuous.

Answer: Continuous

Hard

Graph or Situation

If a graph is shown, the graph decides.

Example
A nurse records a patient’s temperature once each hour.
−5−4−3−2−112345−5−4−3−2−112345xy

Separate points → discrete. A connected line or curve → continuous.

Temperature can be continuous, but this graph shows only separate points.

Nothing is drawn between the points.

Discrete.

Answer: Discrete

1
The height of a sunflower over two months.
−5−4−3−2−112345−5−4−3−2−112345xy
Show Answer

Separate points → discrete. A connected line or curve → continuous.

The graph is a connected curve, and height can fall between whole numbers.

Continuous.

Answer: Continuous

2
The number of whole pizzas a shop sells.
Show Answer

A count of whole objects is discrete. A measurement that can fall between whole numbers is continuous.

You count pizzas. That is a count of whole objects.

Discrete.

Answer: Discrete

3
Is this graph discrete or continuous?
−5−4−3−2−112345−5−4−3−2−112345xy
Show Answer

Separate points → discrete. A connected line or curve → continuous.

The graph is connected.

The values between the points you see are included.

Continuous.

Answer: Continuous

4
The time a student spends on homework.
Show Answer

A count of whole objects is discrete. A measurement that can fall between whole numbers is continuous.

Time can fall between whole numbers, such as 12.5 minutes.

Continuous.

Answer: Continuous

5
A coach records the distance of a runner at five moments.
−5−4−3−2−112345−5−4−3−2−112345xy
Show Answer

Separate points → discrete. A connected line or curve → continuous.

Distance can be continuous, but this graph shows only separate points.

Discrete.

Answer: Discrete

Need help deciding discrete or continuous?

Book a Session with Amy