Math 143 Week 9 Desmos Activity Worksheet (2)
pdf
keyboard_arrow_up
School
Boise State University *
*We aren’t endorsed by this school
Course
143
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
3
Uploaded by AgentCrownDove34
M143 Week 9 Worksheet Math 143 Week 9 Activity Worksheet Inverse Functions Directions: These activity questions are written to follow the Desmos activity for the week. After the weekly lecture class meetings, you should be able to answer these questions. Answer the questions, save the document, and submit the assignment to Canvas. 1.
Explain what it means for a function to have an inverse. Having an inverse means that if you have a function that changes something, the inverse function can change it back to what it was before. It's like pressing a button to turn a light on and another button to turn it off. Not all functions have inverses, but those that do can reverse their actions. 2.
Explain what it means for a function to be one-to-one. A function is one-to-one when each input matches with only one output, and no two different inputs match with the same output. It's like each key on a keyboard only types one letter, and no two keys type the same letter. 3.
Every function has an inverse, but in order for a function to have an inverse that is also a function, it must be one-to-one. Explain why. A function must be one-to-one to have an inverse that is also a function because in a one-to-one function, each input has only one corresponding output, ensuring that the inverse can uniquely reverse the function's action. 4.
Give an example of a function that is one-to-one. Explain. An example of a one-to-one function is f(x)=2x+3. It's one-to-one because each input gives a unique output, and no two different inputs produce the same output.
M143 Week 9 Worksheet 5.
Give an example of a function that is not one-to-one. Explain. An example of a function that is not one-to-one is f(x)=x 2 because different inputs x=−2) can produce the same output (x)=4). 6.
Explain the difference between f
(
x
)
-1
and
f -1
(
x
)
. f(x) −1 deals with the individual outputs of the function f(x), finding their reciprocals. f −
1 (x) represents a whole new function that reverses the original function f(x), mapping outputs of f(x) back to their original inputs. 7.
Explain how to find the equation for the inverse of a function. To find the equation for the inverse of a function f(x): Replace f(x) with y. Swap x and y. Solve for y. Replace y with f −
1 (x) to get the equation for the inverse function.
8.
Explain how to sketch the graph of the inverse of a function. Find the inverse function) f −
1 (x). Swap the x and y coordinates. Plot these points to sketch the inverse function. Check for symmetry around the line y=x. Analyze key features like intersections and turning points. 9.
Given the function 𝑓(𝑥) = √𝑥 + 3
, answer each of the following: a.
What type of function is this? b.
Find the equation for f -1
(
x
). c.
Find the domain and range for both the function and its inverse. b. Sketch the function and it’s inverse on the same set of axis. Make sure to label your window and the graphs. e. Check your equations by typing them into Desmos to verify that they are inverses of each other.
M143 Week 9 Worksheet a)
Type of function: The function f(x)= x+3 is a square root function. It's a type of radical function where the input is under the square root symbol. b)
Equation for f −1 (x): To find the inverse, we switch x and y: y= x+3 Swap x= y+3 Square both side to isolate y: x2=y+3 y=x2-3 Thus, the equation for f −1 (x) is f −1 (x)=x 2 −3.
c)
Domain x ≥
-3 Range ≥
0 for it inverse Domain = all real numbers x Range= y ≥
-3 d)
n/a e)
You can use Desmos or any other graphing tool to plot the functions and verify that they are indeed inverses of each other. The graph of f(x) should reflect across the line y=x to match the graph of f −1 (x).
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help