This module provides practice problems designed to develop some concepts related to horizontal and vertical permutations of functions by graphing.
In a certain magical bank, your money doubles every year. So if you start with $1, your money is represented by the function
$M={2}^{t}$ , where
$t$ is the time (in years) your money has been in the bank, and M is the amount of money (in dollars) you have.
Don puts $1 into the bank at the very beginning (
$t=0$ ).
Susan
also puts $1 into the bank when
$t=0$ . However, she also has a secret stash of $2 under her mattress at home. Of course, her $2 stash doesn’t grow: so at any given time t, she has the same amount of money that Don has, plus $2 more.
Cheryl, like Don, starts with $1. But during the first year, she hides it under
her mattress. After a year (
$t=1$ ) she puts it into the bank, where it starts to accrue interest.
Fill in the following table to show how much money each person has.
t=0
t=1
t=2
t=3
Don
1
Susan
3
Cheryl
1
1
Graph each person’s money as a function of time.
Below each graph, write the function that gives this person’s money as a function of time. Be sure your function correctly generates the points you gave above! (*For Cheryl, your function will not accurately represent her money between
$t=0$ and
$t=1$ , but it should accurately represent it thereafter.)
The function
$y=f\left(x\right)$ is defined on the domain [–4,4] as shown below.
What is
$f\left(\mathrm{\u20132}\right)$ ? (That is, what does this function give you if you give it a -2?)
What is
$f\left(0\right)$ ?
What is
$f\left(3\right)$ ?
The function has three zeros. What are they?
The function$g\left(x\right)$is defined by the equation:$g\left(x\right)=f\left(x\right)\mathrm{\u20131}$. That is to say, for any x
-value you put into$g\left(x\right)$, it first puts that value into$f\left(x\right)$, and then it subtracts 1 from the answer.
What is
$g\left(\mathrm{\u20132}\right)$ ?
What is
$g\left(0\right)$ ?
What is
$g\left(3\right)$ ?
Draw
$y=g\left(x\right)$ next to the
$f\left(x\right)$ drawing above.
The function$h\left(x\right)$is defined by the equation:$h\left(x\right)=f(x+1)$. That is to say, for any x
-value you put into$h\left(x\right)$, it first adds 1 to that value, and then it puts the new x
-value into$f\left(x\right)$ .
What is
$h\left(\mathrm{\u20133}\right)$ ?
What is
$h\left(\mathrm{\u20131}\right)$ ?
What is
$h\left(2\right)$ ?
Draw
$y=h\left(x\right)$ next to the
$f\left(x\right)$ drawing to the right.
Which of the two permutations above
changed the domain of the function?
On your calculator, graph the function
$Y1={x}^{3}\u201313x\u201312$ . Graph it in a window with x going from –5 to 5, and y going from –30 to 30.
Copy the graph below. Note the three zeros at
$x=\mathrm{\u20133}$ ,
$x=\mathrm{\u20131}$ , and
$x=4$ .
For what x-values is the function
less than zero? (Or, to put it another way: solve the inequality
${x}^{3}\u201313x\u201312<0$ .)
Construct a function that looks exactly like this function, but moved
up 10. Graph your new function on the calculator (as Y2, so you can see the two functions together). When you have a function that works, write your new function below.
Construct a function that looks exactly like the original function, but moved
2 units to the left. When you have a function that works, write your new function below.
Construct a function that looks exactly like the original function, but moved
down 3 and
1 unit to the right. When you have a function that works, write your new function below.
Questions & Answers
where we get a research paper on Nano chemistry....?
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest.
Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.?
How this robot is carried to required site of body cell.?
what will be the carrier material and how can be detected that correct delivery of drug is done
Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?