Question

The graph above represents a step function. A graph of a step function resembles steps of a staircase because it does not represent continuous data. The black dot represents a closed endpoint (to include) and the white dot represents an open endpoint (do not include).

Use the graph to determine and select how much it costs to park for 121 mins?
a.
$3
c.
$9
b.
$6
d.
$12

Answer 1

From the graph, it costs $6 to park for 121 mins.

Answer 2

We have been given the step function:

We need to find the function from the given graph

The function will be
`3\left \lceil (x)/(2) \right \rceil`

Whenever we put different values of y we will get the values of y which should be the value according to the graph.

We will convert 121 min in hours since, graph shows the x-axis in hours.

`121\text{minutes}=(121)/(60)=2.01` hours

So, since we need to find cost to park for 121 minutes or 2.01 hours we will put x=2.01 in the formed function above:

`3\left \lceil (2.01)/(2) \right \rceil`

`3\left \lceil 1.005 \right \rceil`

And
`\left \lceil 1.005 \right \rceil=2` being a floor function which always consider the next integer to the decimal inside the function.

`3\cdot 2`

`6` is the cost for 121 minutes or 2.01 hours

Therefore, option c is correct that is $6.