Question 242·Easy·Algebra

The phrase "for every minute of the ride" tells you which number should be multiplied by $m$. Which number is that?

Once you have an expression for the total cost using $m$, write it as $g(m) = \text{(your expression)}$ and compare it to the answer choices.

Pick a simple ride length, such as $m = 10$ minutes. Using the words from the problem, calculate the cost by hand: start with the flat fee of $3 and then add $0.50 for each of the 10 minutes.

In Desmos, type each function on its own line, for example:

• g1(m) = 0.50m - 3
• g2(m) = 3m + 0.50
• g3(m) = 3m - 0.50
• g4(m) = 0.50m + 3

In Desmos, make a table or just evaluate each function at $m = 10$ (for example, type g1(10), g2(10), etc.). The correct function is the one whose value at $m = 10$ matches the cost you computed directly from the description.

The problem describes two parts of the total cost:

• A flat fee of $3 (this is paid no matter how many minutes the ride lasts).
• A per-minute charge of $0.50 for each minute of the ride.

So the total cost is "flat fee + (cost per minute) × (number of minutes)."

Let $m$ be the number of minutes.

• The per-minute part is $0.50$ dollars for each minute, so that part is $0.50m$.
• The flat fee is $3$ dollars.

So the total cost is modeled by the expression $0.50m + 3$.

We are asked for a function $g$ that gives the total cost in dollars of a ride lasting $m$ minutes.

From step 2, the total cost is $0.50m + 3$, so in function notation this is

This corresponds to answer choice D.