Reading Domain and Range from a Graph

How far it spreads, and how high it reaches.

11 problems · about 22 minutes · F-IF.A.2, F-IF.B.5

What this lesson teaches

The student reads domain and range from a graph and from a context.

The domain is the set of accepted inputs; the range is the set of produced outputs.
A square is never negative, which puts a floor under its range.
Context can restrict both beyond whatever the algebra permits.

Straightforward practice. Get the method working first.

4 problems

y = x² + 2. Smallest output?
Answer 2
Why 2.
y = x² − 4. Smallest output?
Answer -4
Why 0 minus 4.
y = −x². Largest output?
Answer 0
Why It opens downward.
y = 3x + 1. Is the domain every real number? 1 for yes, 0 for no.
Answer 1
Why A line has no gaps.

The same ideas with more to keep track of.

3 problems

A function counts children in a class. Can the input be −2? 1 for yes, 0 for no.
Answer 0
Why Context restricts it.
y = x² + 9. Smallest output?
Answer 9
Why The floor lifts.
Match each idea to what it describes.
Answer Domain → Every input accepted; Range → Every output produced
Why Inputs come first, alphabetically and logically.

Mixed problems. Work out what kind of question it is before you start.

4 problems

y = −x² + 6. Largest output?
Answer 6
Why The peak.
A ticket price function takes whole tickets only. Is the domain every real number? 1 for yes, 0 for no.
Answer 0
Why Whole numbers only.
The Floor: For y = x², what is the smallest possible output?
Answer 0
Why 0.
The Lifted Floor: For y = x² + 5, what is the smallest possible output?
Answer 5
Why 5.