A sporting goods store is having a 15% off sale on all items. Which functions can be used to find the sale price of an item that has an original price of x? You may choose more than one correct answer

Question

y = .85 x

ƒ( x) = 1.15 x

Sale = Original - 15

ƒ( x) = x - .15 x

Sale = Original - .15(Original)

Answer 1

y =.85x new price is 85% of the prediscount price.

f(x) = x-.15x = .85x is another correct answer x(1-.15) = .85x

Sale = Original - .15(Original) is another correct answer

Answer 2

Hi,

Here are steps:

Q: What is the sale price?

(The problem also wants the answer to be written in functional notation, such as using f(x)= y for the sale price.)

1. Let original price= x
2. Let f(x)=y=sale price

Note: 15%= .15. or 15/100. Also, f(x)=y

3. Then sale price=f=f(x)= y=original price - .15(x)

Now just use substitution: y= 1x - .15x=.85x

Note: 1-.15=.85. y=.85x. Answer

Here are a few reflective questions:

Q: Is this answer, y=.85x, a function?

Yes, because for every new item value used in the equation, there will be a unique value for the sale price “y.”

Here is another question:

Q: What would this equation and function look like on a coordinate graph?

Enter the equation, y=.85x into a graphing calculator.

(Look for the Y= , which is the first top key.

Also, “x” is to the first power. If you said that you have a linear function, you would be correct.)

Q: How would you use the graphing table to examine data from the equation= y=.85x?

Answer: After graphing the equation, check the last function button called, GRAPH. Then press blue key called 2nd and, then the Graph Key, which also reads in blue the word TABLE.

You will see an “x” and “y” table for the function, y=.85x.

Q: Do you need any zero value for the “x” value?

No, unless the store owner is giving away items for no cost.

Do you need negative values or “x”?

No, the money is positive.

Let’s us use 1 from graphing calculator table?

Q: What would the sale price “y” be?

Let “x” = 1 = $1, then how much would you get the item for if you used f(x)=f(1)=.85x= .85($1)= 0.85 cents

Answer: Look at the “y” value, the sale price, which is $0.85

($1, 0.85). Answer sale price is 85 cents.