Question

What’s the function of this?

Answer 1

The hint about this being a linear function is a critical piece of information.

A linear function has a fixed slope, so you can use the slope formula to find that slope using the two given points, (-3,-5) and (-1,-1).

`m=(y_2-y_1)/(x_2-x_1) = (-1-(-5))/(-1-(-3)) = (4)/(2)=2`

Now you can use that slope and a point to find the equation of the function.

g(x) = mx + b, but m=2, so g(x) = 2x + b

If we plug in one of the points, we can calculate b:

-5 = 2(-3) + b

-5 = -6 + b

1 = b

Now you have your function: g(x) = 2x + 1

You can use it to calculate the missing values in the table.