112k views
4 votes
BOAT RENTAL The cost to rent a paddle boat at the county park is $8 per hour plus a nonrefundable deposit of $10. The cost can be modeled by the function f(h)=8h+10 , where h represents the number of hours the boat is rented. Describe the graph of g(h) as it relates to f(h) if the nonrefundable deposit increases to $15.

g(h)=____is the translation of f(h)____ units ___

1 Answer

2 votes

Final answer:

The function g(h) = 8h + 15 reflects an increase of the nonrefundable deposit from $10 to $15, resulting in the graph of f(h) being translated upward by 5 units.

Step-by-step explanation:

The student has provided an equation f(h) = 8h + 10, which represents the cost to rent a paddle boat, with h representing the number of hours the boat is rented. The initial function includes an $8 per hour rental fee plus a $10 nonrefundable deposit. If the nonrefundable deposit increases to $15, the new function would be g(h) = 8h + 15. This change in the deposit results in a vertical translation of the graph of f(h) upward by 5 units, as the only change is in the constant term (the y-intercept) of the linear equation.

The graph of the function g(h) can be obtained by translating the graph of the function f(h) by 5 units in the vertical direction. This is because the nonrefundable deposit has increased from $10 to $15, which will increase the value of g(h) by $5 for any given value of h.

Thus, the graph of g(h) is f(h) translated 5 units up. The equation that represents g(h) is g(h) = f(h) + 5.

User Naftis
by
7.8k points