Question

An electrician charges a base fee of $70 plus $45 for each hour of work. The minimum the electrician charges is $160. Create a table that shows the amount the electrician charges for 1, 2, 3, and 4 hours of work. Determine the domain and range of the relation in context and explain whether or not this represents a function.

Answer 1

1) See below for table.

2) Domain:
`\{1, 2, 3, 4\}`

Range:
`\{160, 160, 205, 250\}`

Yes, this is a function.

Explanation:

We know that the electrician charges a base fee of $70 plus $45 for each hour of work.

We also know that the minimum the electrician charges is $160.

Let's write an equation. Let x denote the number of hours worked and y denote the total price. There's also a base fee of $70. So, we can write the following equation:

`y=45x+75`

Part 1)

Let's create our table for 1, 2, 3, and 4 hours. To do so, we simply need to substitute each value for x in our equation.

1 Hour:

We have:

`y_1=45(1)+70`

Multiply and add:

`y_1=45+70=\$115`

However, notice that the minimum the electrician charges is $160. Therefore, for one hour of work, the electrician will still charge $160. So:

`y_1=\$160`

2 Hours:

Substitute 2 for x:

`y_2=45(2)+70=90+70=\$160\\`

So:

`y_2=\$160`

3 Hours:

Substitute 3 for x:

`y_3=45(3)+70=135+70=\$205`

So:

`y_3=\$205`

4 Hours:

Substitute 4 for x:

`y_4=45(4)+70=180+70=\$250`

So:

`y_4=\$ 250`

Therefore, for 1, 2, 3, and 4 hours of work, the prices will be $160, $160, $205, and $250, respectively.

We can create the following table (please scroll down to see the table. Also, y is measured in dollars).

Part 2)

The domain of a relation are the input values.

In this context, our input values are the amount of hours worked, and we calculated for 1, 2, 3, and 4 hours of work.

Therefore, our domain in this context is:

`\{1, 2, 3, 4\}`

The range of a relation are the output values.

In this context, the output values are the price for x hours of work.

Therefore, our range in this context is:

`\{160, 160, 205, 250\}`

This relation does represent a function. Remember that a function cannot have repeating input values. In other words, no one input can be equal to two or more different outputs. However, one output can be mapped to two or more different inputs.

For our table, none of the inputs are repeating. So, our relation is a function.

And we're done!