Question

The function f(x) = 0.6x shows the relationship between the original price, x, in dollars, and the discounted price, f(x), in dollars, of all clearance items at Max’s Music Store.

A) What is the discounted price of an item originally priced at $50?
B) If the discounted price of an item is $30, what was its original price?
C) If the original price of an item is $80, what is the discounted price?
D) Calculate the slope of the line representing this function.

Answer 1

A) The discounted price of an item originally priced at $50 is $30.

B) If the discounted price of an item is $30, its original price was $50.

C) If the original price of an item is $80, the discounted price is $48.

D) The slope of the line representing this function is 0.6.

Step-by-step explanation:

A) To find the discounted price for an item originally priced at $50, we can use the function:
`\( f(50) = 0.6 * 50 = 30 \)`. Therefore, the discounted price is $30.

B) If the discounted price of an item is $30, we can use the inverse of the function to find the original price:
`\( x = (30)/(0.6) = 50 \)`. So, the original price was $50.

C) For an original price of $80, applying the function gives
`\( f(80) = 0.6 * 80 = 48 \)`. Hence, the discounted price is $48.

D) The slope of the line representing the function is the coefficient of
`\( x \)` in the function, which is 0.6. The slope represents the rate of change, indicating that for every increase of $1 in the original price, the discounted price increases by $0.6.