Question

12. Determine if the relation represents y as a function of x. If it is a function, identify the domain and the range. More than one answer may be correct, select all that apply.

Answer 1

Answer:$\begin{gathered} \begin{equation*} Domain:\text{ -\infty}\leq\text{x}\leq\text{\infty} \end{equation*} \\ Range:\text{ -\infty}\leq y\leq\text{\infty} \end{gathered}$Explanation:

Domain is the set of valid inputs to a function

Range is the set of all the valid outputs

For the polynomial graph:

$\begin{gathered} Domain\text{ = \lparen-4, \infty\rparen} \\ Range\text{ = \lbrack-4.33, \infty\rparen} \end{gathered}$

For the line graph:

$\begin{gathered} Domain=(-∞,\text{ -2\rparen} \\ Range=(-∞,\text{ -3\rparen} \end{gathered}$

For the combined graph:

$\begin{gathered} Domain=(-4,\text{ \infty\rparen U\lparen-\infty, -2\rparen} \\ Domain\text{ = \lparen-\infty, \infty\rparen} \\ \\ Range=(-4.33,\text{ \infty\rparen U\lparen-\infty, -3\rparen} \\ Range\text{ = \lparen-\infty, \infty\rparen} \end{gathered}$

Therefore, the domain and the range for the graph are:

$\begin{gathered} Domain:\text{ -\infty}\leq\text{x}\leq\text{\infty} \\ Range:\text{ -\infty}\leq y\leq∞ \end{gathered}$