Question

Find the equation of the graph in function notation. Name your function "f" and use x as your variable. ​

Answer 1

see explanation

Explanation:

The equation of a line in slope- intercept form is

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

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (2, 0) ← 2 points on the line

m =
`(0+1)/(2-0)` =
`(1)/(2)`

Note the line crosses the y- axis at (0, - 1) ⇒ c = - 1

y =
`(1)/(2)` x - 1 ← in slope- intercept form

f(x) =
`(1)/(2)` x - 1 ← in functional notation

Answer 2

the equation of the graph should be

f(x)= 1/2x -1