Question

which choice represents a function? a. $x = 4$ b. $y = x - 9$ c. \

$$\begin{tabular}{|c|c|} \\hline $x$ & $y$ \\\\ \\hline $-2$ & $3$ \\\\ \\hline $4$ & $3$ \\\\ \\hline $-1$ & $4$ \\\\ \\hline $-2$ & $4$ \\\\ \\hline $5$ & $5$ \\\\ \\hline \\end{tabular}$$

d. $\\{(2, 3), (4, 5), (6, 7), (2, 9), (3, 10)\\}$

Explanation:

Step1: Recall function definition

A relation is a function if each input ($x$-value) has exactly one output ($y$-value).

Step2: Analyze Option A

$x=4$ is a vertical line; one $x$-value maps to infinite $y$-values. Not a function.

Step3: Analyze Option B

For $y=x-9$, every $x$-value gives exactly one $y$-value. This is a function.

Step4: Analyze Option C

The table has $x=-2$ mapping to $y=3$ and $y=4$. Not a function.

Step5: Analyze Option D

The set has $x=2$ mapping to $y=3$ and $y=9$. Not a function.

Answer:

B. $y = x - 9$