Question

Introudction to functions

Answer 1

f(x) =
`(3)/(2)` x - 1

Explanation:

a linear function has slope- intercept form

f(x) = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (4, 5) and (x₂, y₂ ) = (- 2, - 4) ← 2 ordered pairs from the table

m =
`(-4-5)/(-2-4)` =
`(-9)/(-6)` =
`(3)/(2)`

the point (0, - 1 ) from the table represents the y- intercept , so c = - 1

f(x) =
`(3)/(2)` x - 1 ← represents the function