Question

Create the f(x) function based on the table. Your answer should be in function notation. X f(x) - 10 -6 -9 -5 1-8 -4 -7 1-3 5 9​

Answer 1

Answer:

$f(x) = x + 4$

Step-by-step explanation:

First create an equation in slope-intercept form, y = mx + b. To do this, find the rate of change or slope (m), and the y-intercept (b).

Using two pairs, (-7, -3) and (-8, -4),

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 -(-3)}{-8 -(-7)} = \frac{-1}{-1} = 1$

m = 1

To find b, substitute m = 1, x = -7 and y = -3 into y = mx + b.

Thus:

-3 = (1)(-7) + b

-3 = -7 + b

-3 + 7 = b

4 = b

b = 4.

Replace y with f(x), m with 1 and b with 4 in y = mx + b.

The function would be:

$f(x) = x + 4$