Integrated 1 Week 5 (September 21-25) 1.2.1 What is the function?
Function Machines
In the previous lesson, you used equations relating two variables (like y=3-2x) to make graphs and find
information. Today you will look more closely at how what equation do I write? equations that relate two variables help establish a function
between the variables. You will also learn a new notation to help represent these functions.
1-33. ARE WE RELATED?
Examine the table of input (x) and output (y) values below. Is there a relationship between the input and output
values? If so, write an equation for this relationship.
-1
0
1
2
3
5
4
5
input (x)
output (y)
3 8
-4
-1
2
5
8
14
11

Aprojectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = -16t2 + 704t. after how many seconds does the projectile take to reach its maximum height?

The function models the number of accidents

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?