A company charges $15 per hour plus a $20 setup fee to rent a bouncy house for 3 hours or less. They charge $12 per hour and no setup fee if the bouncy house is rented for more than 3 hours. Sketch a graph of the piecewise function that models this scenario. Use the graph to select the correct equation for the function where x

Question

is the number of hours and y
is the total cost.(1 point)
Responses

y={15+20, 0<x≤312, x>3
y equals left brace line 1 15 plus 20 comma 0 less than x less than or equal to three line 2 12 comma x greater than 3

y={15x+20, 0<x<312x, x≥3
y equals left brace line 1 15 times x + 20 comma 0 less than x less than three line 2 12 times x comma x greater than or equal to 3

y={15x+20, 0<x≤312x, x>3
y equals left brace line 1 15 times x plus 20 comma 0 less than x less than or equal to three line 2 12 times x comma x greater than 3

y={15+20x, 0<x≤312, x>3
y equals left brace line 1 15 plus 20 times x comma 0 less than x less than or equal to three line 2 12 comma x greater than 3
Remaining Attempts : 3
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Answer 1

To model the total cost of renting the bouncy house using a piecewise function, we can define it based on the number of hours rented:

1. If the number of hours \( x \) is greater than 0 and less than or equal to 3, the total cost \( y \) can be expressed as: \[ y = 15x + 20 \] Here, $15 per hour comes from the hourly rate, and the $20 is the setup fee.

2. If the number of hours \( x \) is greater than 3, the total cost \( y \) is: \[ y = 12x \] In this case, there's no setup fee, and the cost is simply $12 per hour.

Thus, the complete piecewise function can be written as: \[ y = \begin{cases} 15x + 20 & 0 < x \leq 3 \ 12x & x > 3 \end{cases} \]

Now, analyzing the options provided, we see that the correct equation for the piecewise function is:

\[ y = \begin{cases} 15x + 20 & 0 < x \leq 3 \ 12x & x > 3 \end{cases} \]

So the correct response is:

y={15x+20, 0<x≤3; 12x, x>3} y equals left brace line 1 15 times x plus 20 comma 0 less than x less than or equal to three line 2 12 times x comma x greater than 3