Write the function representing the graph

The function representing the graph is described by two equations, depending on the "x" value

f(x) = (1/3)x + 3 , if x is greater than -3.

f(x) = -x - 5 , if x is less than -3.

Step-by-step explanation:

First, you have to realize that the graph is described by two functions depending on the "x" value and that it is not defined in x= -3.

Then, for "x" values greater than -3, we look at the right line and we took 2 couple of points (-3,2) and (0,3). Using the formula for the slope and the interception with y axis

Slope = y2- y1 / x2- x1 = 3 - 2/ 0 - (-3) ⇒ slope = 1/3.

Interception with "y" axis y= 3

⇒ f(x) = (1/3) x + 3.

For "x" values minor than -3, we have to look the left line. Here we used the slope formula and points (-3, -2) and (-5, 0)

Slope = 0 - (-2)/ -5 - (-3) =-1. So, f(x) = -x + b.

Finally we use one of the points to replace in the formula of f(x) to find "b".

-2 = - (-3) + b ⇒ b = -5. ⇒ f(x) = - x -5

Summarizing, f(x) = (1/3)x + 3 , if x is greater than -3.

                      f(x) = -x - 5 , if x is less than -3.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .