Question

The following graph is a linear function comparing the inches of snowfall to hours of time in a specific location.

(a) What is the domain of the function? Express it as an inequality.

(b) What is the range of the function? Express it as an inequality.

Answer 1

Domain:

`0\leq x\leq5`

Range:

`0\leq y\leq 10`

Explanation:

The domain of a function is the span of the x-values the graph covers, the the range of a function is the span of the y-values the graph covers.

DOMAIN:

We can see that the span of x-values covered spans from x=0 to x=5.

In other words, our domain is all numbers between x=0 and x=5 including x=0 and x=5.

So, we write this as a compound "and" inequality. This would be:

`0\leq x\leq5`

This is interpreted as all numbers greater than or equal to 0 and less than or equal to 5.

RANGE:

We can see that the span of y-values spans from y=0 to y=10.

So, same thing, our range will be all numbers between 0 and 10 including 0 and 10.

Again, as a compound inequality, this is:

`0\leq y\leq 10`

In words, this means all y-values greater than or equal to 0 and less than or equal to 10.

Note that we use y this time since we're discussing the range.

And we're done!