Question

Part a: How many pieces are in the step functionpart b: how many intervals make up the step function? What are the interval valuespart c: why do we use open circles in some situations and closed in otherspart e are the pieces of this piecewise function linear or non linear?part f what is the range of this piecewise function?

Answer 1

a) The step function seen in the figure has 6 pieces, one for each step

b) There are 6 intervals, one for each piece. Their values are:

(0, 1]

(1, 2]

(2, 3]

(3, 4]

(4, 5]

(5, 6]

c) The open circles indicate that the endpoint is not included in the interval. The closed circles indicate the endpoint is included in the interval.

For example, in the second interval, 1 is not included (open circle) and 2 is included (closed circle).

d) This is a function because for eac value of x there iss one and only one of y. If the open circles were closed circles, then thi wouldnot be a function.

e) All the pieces are linear because their graph is a line (flat horizontal line)

f) The range of the function is the set of output values:

Range = {46, 48, 50, 32, 54, 56}