Question

A function f(x) is graphed on the coordinate plane.

Answer 1

Answer: y = - 4x + 2

Explanation:

The graph shows a linear function, which is a first degree polynomial, whose form is ax + b.

The rule or fucntion is f(x) = y = ax + b. This form is called the slope-intercept form, because the coefficient a is the slope of the line and b is the y-intercept.

The graph permits you to calculate both parameters.

1) The slope, a is defined in this way:

• a = rise / run = [change in y] / [change in x] = [y₂ -y₁] / [x₂ - x₁]

• you can use the points (0, - 2) and (-1,2):

       ⇒ a = [ 2 - (-2) ] / [ -1 - 0 ] = 4 / (-1) = - 4

2) b, the y-intercept, is the value of the function, y, when x = 0. In the graph you can see that this is - 2. b =  - 2.

3) Substituting the values of a and b in the form y = ax + b, you the rule:

• y = - 4x - 2

Answer 2

Answer:

f(x) = -4x - 2

Step-by-step explanation:

slope = -4 and y intercept = -2