Solve each problem. See Example 4. Suppose that the cost of maili...

Question

Solve each problem. See Example 4. Suppose that the cost of mailing a letter weighing x ounces, where x>0, is ƒ(x)=55-15[[1-x]]cents. What is the cost of mailing a 2.6-ounce letter?

Accepted Answer

Hey, everyone in this video, we're gonna work through the following problem. The cost of X ounces or X is greater than zero of T is expressed as F of X is equal to 45 minus 12, multiplied by the floor of three minus X cents. We're asked to find the cost of 3.5 oz of teeth. We're given four answer choices. Option A is 57 cents. Option B is 93 cents. Option C is 33 cents and option D is 12 cents. Now, we're given That X is the number of ounces of T and we want to find the cost for 3.5 oz and that means that our X is going to be equal To 3.5 oz. And we're giving our function f of X is equal to 45 - multiplied by the floor of three -X. Ok. So these double square brackets indicate the floor function or sometimes it's also called the greatest integer function. Now, this function gives the cost of X ounces. We wanna find the cost of 3.5 ounces. So we're gonna substitute X equals 3.5 into this function and simplify the result. So the function F Evaluated at 3. is equal to 45 minus Multiplied by the floor of 3 -3.5. OK. Now, before we can determine the value of this floor function, what we wanna do is simplify inside. OK. So we have 45 - multiplied by the floor of -0.5. Now the floor of -0.5, what is that equal to? Well, if we think of it as a floor function, you can think of the floor as being underneath you. OK? It's under your feet. So the floor function takes the integer that is underneath the value that we're at. So negative 0.5, the next integer underneath it is going to be negative one. Now, if we want to think of this as the greatest integer function and we can think of a number line and on our number line, we're gonna draw two, 10, -1, OK? Going from right to left and we're gonna draw negative 0.5 on this number line right between negative one and zero and the greatest integer function tells us to take the greatest integer less than the value. OK? So the value we have is negative 0.5 an integer that is less than that is gonna be to the left. So we're gonna move to the left from our starting position and we're gonna stop when we hit the first integer and the first integer we hit when we do that is negative one. OK? So whichever way you think about this function, you're gonna get the same result. And that in this case is negative one. So we have 45 - multiplied by -1. Let me simplify, we have 45 plus 12 And which gives us 57 cents. OK? So using the function, we found that the cost of 3.5 ounces of tea is cents, which corresponds with answer choice. A thanks everyone for watching. I hope this video helped see you in the next one.

Solve each problem. See Example 4. Suppose that the cost of mailing a letter weighing x ounces, where x>0, is ƒ(x)=55-15[[1-x]]cents. What is the cost of mailing a 2.6-ounce letter?

Key Concepts

Function Notation

Piecewise Functions

Substitution

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