{Use of Tech} Height and time The height in feet of a baseball...

Question

{Use of Tech} Height and time The height in feet of a baseball hit straight up from the ground with an initial velocity of 64 ft/s is given by h= ƒ(t) = 64t - 16t² where t is measured in seconds after the hit.

a. Is this function one-to-one on the interval 0 ≤ t ≤ 4?

a. Is this function one-to-one on the interval 0 ≤ t ≤ 4?

Accepted Answer

Welcome back everyone. In this problem, a share market opens at 9 AM and closes at 3 PM. The price of a share for a particle share on a given date is p of x equals 12 x minus 2 x squared. Where x is the number of hours from 9 AM. And we want to find whether p of x is a one to one function on the interval where x is greater than or equal to 0 and less than or equal to 6. For our answer choices, a says that p of x is a one to one function. B says that p of x is not a one to one function. And c says there's that says that there's not enough information. Now, what do we want to know here? Well, we want to determine whether p of x is a one to one function. And recall that a one to one function means that for each input there is a single unique output. So what that means, if I were to map it out, it's saying that for our domain, which in other words is our input And for our range, which is our output, if I have 3 values in my domain and 3 values in my range, then for a one to one function, each input would map to 1 output. Now, that's what we want to test here. In other words, are there only unique values for p of x on this interval? Can we find different values for this interval where p of x is the same? Well, let's test it out. Let's start with the first value on the interval. 0. So when x equals 0, then p of 0 equals 12 multiplied by 0 minus 2 multiplied by 0 squared. 12 multiplied by 0 is 0. 2 multiplied by 0 squared is 0. So that tells us p of 0 equals 0. Are there any other times where we can input a value or substitute a value for x that would make our function p equals 0? Well, how about we check p of 6? When x equals 6, then p of 6 equals 12 multiplied by 6 minus 2 multiplied by 6 squared. 12 multiplied by 6 equals 72. 6 squared is 36 and 36 multiplied by negative 2 equals negative 72 and 72 minus 72 equals 0. So what is this telling us? Well, now, it's telling us that for the both of these different values of x, in other words, when x is 0 and x is 6, then both of them have the same output or both of p of x has the same value for both of these functions. So that tells us that p of x is not a one to one function because it does not have a unique input for each unique output. So, our answer would have been answer choice b. Thanks for watching everyone. I hope this video helped.

{Use of Tech} Height and time The height in feet of a baseball hit straight up from the ground with an initial velocity of 64 ft/s is given by h= ƒ(t) = 64t - 16t² where t is measured in seconds after the hit.

a. Is this function one-to-one on the interval 0 ≤ t ≤ 4?

Key Concepts

One-to-One Function

Quadratic Functions

Critical Points and Intervals

Watch next