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Lesson · Grade 10 · Foundations of Mathematics and Pre Calculus

Domain and Range from a Graph and a Situation

  • Grade 10
  • Foundations of Mathematics and Pre Calculus
  • 2 min 8 s
  • British Columbia
  • BC10-MA-09

A parabola drawn from x = −2 to x = 5 casts a shadow on each axis, giving a domain of −2 ≤ x ≤ 5 and a range of −1 ≤ y ≤ 7. A 4-hour hike at 3 km each hour then gives a domain of 0 ≤ t ≤ 4 and a range of 0 ≤ d ≤ 12; the video also corrects the mistake of swapping domain and range, and shows that tickets sold can only be whole numbers from 0 to 8.

Concept: Domain and range from a graph and from a situation

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In one sentence

The question this lesson answers

Here is the graph of a function. Which x values and which y values does it use?

The graph starts at x equals negative 2 and stops at x equals 5. Solid dots mean both ends are included.

Transcript

What the lesson says

Here is the graph of a function. Which x values and which y values does it use?

The graph starts at x equals negative 2 and stops at x equals 5. Solid dots mean both ends are included.

The domain is all the x values, the inputs. The graph's shadow on the x-axis runs from negative 2 to 5.

So the domain is negative 2 less than or equal to x, less than or equal to 5.

The range is all the y values, the outputs. The graph's shadow on the y-axis runs from the lowest point, negative 1, to the highest, 7.

So the range is negative 1 less than or equal to y, less than or equal to 7.

Now a situation: a hiker walks 3 kilometres each hour for 4 hours, so 3 times 4 is 12 kilometres.

Time, t, is the input. The hike lasts 4 hours, so the domain is 0 less than or equal to t, less than or equal to 4.

Distance, d, is the output, so the range is 0 less than or equal to d, less than or equal to 12 kilometres.

A common mistake is to swap them. The domain is not 0 to 12: that is the distance, so it is the range.

The domain is the inputs, along the horizontal axis. The range is the outputs, up the vertical axis.

Time can be any value from 0 to 4, like 2.5 hours, but you cannot sell half a ticket.

With 8 seats to sell, the domain for tickets sold is the whole numbers 0 to 8: dots, not a solid line.

So the domain is all the inputs, the x values, and the range is all the outputs, the y values.

Curriculum

Where this fits

British Columbia, Grade 10

Foundations of Mathematics and Pre Calculus 10, Functions: functions and relations: connecting data, graphs, and situationsBC10-MA-09

Previous: The vertical line testNext: Function notation: what f(3) means

The outcomes and strands follow the British Columbia curriculum.

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