Question

Write a rule for the linear function in the table.
x f(x)
–3 –1
0 2
3 5
6 8



A. f(x) = x + 2


B. f(x) = 3x


C. f(x) = x – 2

Answer 1

Try substituting the given values for x in each of the choices. For example what do you get when you put x = -3 into the equation in choice A?

Answer 2

Carrying onsubstituting into equation in choice A:
f(-3) = -3 + 2 = ?

Answer 3

f(-3)= -3 + 2 = -5

Answer 4

-3 + 2 = -1, not -5
-3 - 2 = -5

Answer 5

ohh ok i got it

Answer 6

Think of your table as a bunch of points on a line (a linear function is one that is graphed by a line). Let y = f(x). Now you can use any two points in the table to compute the formula for that line.

Let's use (0,2) and (6,8). By the slope formula,
\[m=\frac{y_2-y_1}{x_2-x_1} = \frac{8-2}{6-0} = 1\]

So our line will be of the form y = 1x + b

Now just plug in one of those points to find the value of b, and we're done!
\[2 = 1(0) + b\rightarrow b = 2\]
So our function is described by
y = f(x) = 1x + 2 = x + 2

Answer 7

Most of the time you don't actually get to choose from a handful of answers :-)

Answer 8

ok thanks

Answer 9

If you are allowed to choose from a set of choices, a good point to try to weed out some of the possibilities is x = 0. The arithmetic is easy, and in this case, it gives you the answer because only one of them works. Sometimes you'll have to try another point as well, but you might have fewer choices after eliminating any that don't work with x = 0.