Question

Consider the following piece-wise function. Which of the below correctly describes the graph shown?

Answer 1

C

Explanation:

The function is formed of 2 straight lines

The equation of a straight line in slope- intercept form is

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

Calculate the slope using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 4, - 5) and (x₂, y₂ ) = (2, - 2) ← endpoints of left line

m =
`(-2+5)/(2+4)` =
`(3)/(6)` =
`(1)/(2)`

Note the line crosses the y- axis at (0, - 3) ⇒ c = - 3

y =
`(1)/(2)` x - 3 for x < 2 ( arrow on line points left )

Repeat

with (x₁, y₁ ) = (2, - 2) and (x₂, y₂ ) = (3, 1) ← 2 points on right line

m =
`(1+2)/(3-2)` =
`(3)/(1)` = 3, thus

y = 3x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (3, 1), then

1 = 9 + c ⇒ c = 1 - 9 = - 8

y = 3x - 8 for x ≥ 2 ( arrow on line points right )