Math Snap

STEP 1

What is this asking?
What's the base price to rent a vacuum, before even starting to use it?
Watch out!
Don't get tricked into thinking the number multiplied by $x$ is the flat fee!

STEP 2

1. Define the function
2. Analyze the function
3. Calculate the flat fee

STEP 3

Alright, so we've got this super cool function, $f(x) = 6 \cdot x + 14$, that tells us the total cost to rent a vacuum cleaner.
Here, $x$ is the amount of time the vacuum is rented for, and $f(x)$ spits out the total cost.

STEP 4

Let's break down this function piece by piece.
We've got two parts here: $6 \cdot x$ and $+ 14$.
The $6 \cdot x$ part changes depending on how long we rent the vacuum.
This means $\$6$ is the rate we're charged for each unit of time.

STEP 5

Now, the $+ 14$ part is super interesting!
This part doesn't change, no matter how long we rent the vacuum for.
This is our flat fee!
It's what we pay just for the privilege of using the vacuum, even if we rent it for zero time!

STEP 6

So, to find the flat fee, we need to figure out what $f(x)$ would be if $x = 0$, meaning zero rental time.
Let's plug that into our function:
$$f(0) = 6 \cdot 0 + 14$$

STEP 7

Anything multiplied by zero is zero, so $6 \cdot 0 = 0$.
Now we have:
$$f(0) = 0 + 14$$

STEP 8

Adding zero to a number doesn't change the number, so $0 + 14 = 14$.
This gives us:
$$f(0) = 14$$

STEP 9

So, the flat fee is $\$14$!

The flat fee is $\$14$.