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# Describing Domain and Range

## Describing Domain and Range 1.2 - Solution

a

The domain is all allowed $x$-values of a function. In the coordinate system we find the domain by examining for which $x$-values the function is graphed. Graph $A$ doesn't have any endpoints, which means that it's defined for all $x,$ so it should be paired with domain $3.$ Graph $B$ is drawn between $x=\text{-} 6$ and $x=2.$

This can be written as $\text{-} 6 \leq x \leq 2$, which is domain $2.$ Graph $C$ is plotted from $x=\text{-} 2$ to $x=3,$ where the point at $x=\text{-} 2$ is not closed. This means that the function is defined for each value before, but the $x$-value of the actual point is not included.

Thus, $x$ must then be greater than $\text{-}2$ and less than or equal to $3.$ This is written as $\text{-} 2 < x \leq 3,$ which is domain $1.$ In conclusion, $1-C,\quad 2-B,\quad 3-A.$

b

The range of a function can be derived from the $y$-values of the plotted graph. Graph $A$ has no lower or upper limit, which means the range is all $y,$ range $3.$ Graph $B$ has its maximum value at the left-hand endpoint, where $y=4,$ and its minimum value at the other endpoint, where $y=\text{-} 3$.

Then range is, thus, $\text{-} 3 \leq y \leq 4,$ range $1.$ Graph $C$ has its maximum value at the right-hand endpoint, where $y=6.$ Its minimum value is where $y=\text{-}3.$

Therefore, the range is $\text{-} 3 \leq y \leq 6,$ which is range $2.$ In summary, we have $1-B,\quad 2-C,\quad 3-A.$