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={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+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={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

y={15x+20, 0<x<312x, x≥3

Answer 1

To model the cost of renting a bouncy house as a piecewise function, we can outline the two scenarios based on the number of hours rented:

1. For rentals of 3 hours or less (i.e., $0<x\le 3$):

   • The cost is $y=15x+20$ (where $x$ is the number of hours).

2. For rentals of more than 3 hours (i.e., $x>3$):

   • The cost is $y=12x$.

Thus, we can represent this as a piecewise function:

$$y=\{\begin{array}{lll}15x+20& \text{for }0<x\le 312x& \text{for }x>3\end{array}$$

Now, let's match this with the options given in your responses:

1. $y=15x+20,0<x\le 3;12x,x>3$
2. $y=15+20,0<x\le 3;12,x>3$
3. $y=15+20x,0<x\le 3;12,x>3$
4. $y=15x+20,0<x<3;12x,x\ge 3$

The correct response is clearly the first one:

$$y=15x+20,0<x\le 3;12x,x>3$$