Question

9th grade math What is the function rule? What is the Domain?  What is the Range?

Answer 1

The function rule to this table is a line. We know that a line is given by the equation:

$y=mx+b$

where m is the slope and b is the y-intercept.

To find the slope we use the formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

using the first two points of the table we have that:

$m=\frac{16-10}{2-1}=\frac{6}{1}=6$

Now that we have the slope we need to find the y-intercept. To find it we plug the slope and the values of the third point in the equation and solve for b:

$\begin{gathered} 22=6\cdot3+b \\ b=22-18 \\ b=4 \end{gathered}$

Therefore, the fucntion rule is:

$y=6x+4$

The domain of the function is given by all the values of x it can take:

$(-\infty,\infty)$

The range of the function is given by all the values the y can take:

$(-\infty,\infty)$