Question

PLEASE HELP!!!!

Your friend needs to graph the piecewise function below but does not remember all the steps he/she needs to do. Here is what you friend has come up with. Please double check the work and correct any mistakes you find, then explain why.





Your friend has the following completed for her to graph the piecewise function:

f(x) = 3x – 5 if x < -1

Start with a filled in circle on (-1, -8). Use the slope to go up 3 and right 1 to make another point and drawn the line only going down.

f(x) = -2x + 3 if -1 < x < 4

Put an open circle on (-1,5) and open circle on (4, -5). Connect those points.

f(x) = 2 if x > 4

Put an open in circle on (4,2) then draw a horizontal line to the right.

Answer 1

As per the description of my friend's work, all the steps except the last one are correct.

Step 1 is correct about the slope, the point and the filled circle. We will have the filled circle because the point x=-1 is included too.

Step 2 is correct about the two points with the open circle and that will give us a negative slope. The circle will be open as the two end points are not included.

Step 3 is partially correct in the sense that the "horizontal line to the right" part is correct. What is not correct is the "open circle on (4,2)" part. The circle at x=-4 has to be closed because,
`x\geq-4`, means that the point x=-4 too is included and therefore, there has to be a filled in circle there.

Answer 2

PART 1):

f(x) = 3x – 5 if x < -1

Start with a filled in circle on (-1, -8). Use the slope to go up 3 and right 1 to make another point and drawn the line only going down.

Answer: WRONG.

Because correct inequality is x≤-1 not x<-1. Hence we will put a close circle not an open circle. at (-1,-8).

Also since slope is positive so graph will go upward not downward.

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PART 2):

f(x) = -2x + 3 if -1 < x < 4

Put an open circle on (-1,5) and open circle on (4, -5). Connect those points.

Answer: Correct

Because correct inequality is < or > so both end points will be open circles.

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PART 3):

f(x) = 2 if x > 4

Put an open in circle on (4,2) then draw a horizontal line to the right.

Answer: WRONG.

Because correct inequality is x≥4 not x>4. Hence we will put a close circle not an open circle. at (4,2).