Basic Functions
!) How can f+g(x) be rewritten?
J) How can f/g(x) be rewritten?
!) f(x)+g(x)
J) f(x)/g(x)
!) How can fog(x) be rewritten?
J) What is the difference between o and • in terms of functions?
!) f(g(x))
J) o means to compose and • means to multiply.
!) Find the inverse of y=x
J) Find the inverse of y=2x
!) y=x
J) y=1/2x
!) What does HLT stand for?
J) What does VLT stand for?
!) Horizontal line test
J) Vertical line test
!) What unit is this review based off of?
J) How many subtopics are in this unit?
!) Unit 1
J) 4
E) If f(x)=2x and g(x)=3x-1, what is f+g(x)?
F) If f(x)=4x-1 and g(x)=1x-2, what is f-g(x)?
E) 5x-1
F) 3x+1
E) How is fog(x) said?
F) Can you use graphs for composing functions?
E) f-compose-g of x
F) Yes
E) How do you tell two functions are inverses by looking at table values?
F) Find the inverse of f(x)=-1/3x+1
E) The x-values and y-values are switched for the inverse.
F) f-1(x)=-3x+3
E) What does the VLT prove?
F) What tests must a one-to-one function pass?
E) That an equation is a function.
F) The VLT and HLT
E) What is the name of Unit 1?
F) What month did we start unit 1 in?
E) Functions and Compositions
F) Late January
F) What if fg(x) when f(x)=3x-1 and g(x)=-2x+3
P) What is f-g(x) when f(x)=-x2+7x-4 and g(x)=-x-4
F) -6x2+11x-3
P) -x2-6x
F) What is the highest amount of terms a function can have?
P) Explain how you would evaluate f(g(h(3)))
F) Infinite
P) Plug 3 into h, plug that into g, plug that into f
F) Find the inverse of f(x)=-1/3x+1
P) Find the inverse of g(x)=2x-1
F) f-1(x)=-3x+3
P) g-1(x)=1/2x+1/2
F) Does the function of f(x)=x2+2 have an inverse? Explain your answer.
P) What factors do a one-to-one ratio prove for equations? List 3.
F) No, because the graph does not pass the HLT and crosses the same y-value more than once.
P) That the equation is a function, has an inverse, passes the HLT, passes the VLT.
F) What is a synonym of inverse and how does this apply to inverse functions?
P) Do all linear equations have inverses? If not, explain and give examples.
F) opposite, reverse, applies because an inverse function has the opposite values of the normal function.
P) No, only diagonal linear functions have inverses. Vertical and horizontal functions do not.
A) Given f(x)=-x2+3x+2 and g(x)=2x-1, what is fg(x)?
R) Given f(x)=-x2+3x+2 and g(x)=2x-1, what is f/g(x)?
A) -2x3+7x2+x-2
R) -x2+3x+2/2x-1
A) If f(x)=2x-1 and g(x)=-4x+3, what is f(g(2))?
R) If f(x)=2x-1 and g(x)=-4x+3, what is g(f(2))?
A) -11
R) -9
A) Does the graph of -x2+3x+1 have an inverse? Explain.
R) Explain the 4 steps in finding the inverse of a function.
A) Yes, every x-value has exactly one y-value.
R) 1. rewrite the equation as f(x)= to y=, 2. switch x and y, 3. solve for y, 4. write the new equation in inverse notation.
+A) Explain how to find the inverse of f(x)=√x2-5.
R) Explain how to find the inverse of f(x)=√x+3.
A) They should get f-1(x)=x2+5.
R) They should get f-1(x)=x2-3.
A) Give an example of how function compositions can be used in the real world.
R) Give an example of how inverse functions can be used in the real world.
A) unit conversions, programming, any reasonable answer acceptable.
R) trigonometry, physics, any reasonable answer acceptable.
T) Given f(x)=-x2+3x+2 and g(x)=2x-1, what is fg(x)?
Y) If f(x)=4x, g(x)=2x-1, and h(x)=-x+2, what is fgh(x)?
T) 2x3+7x+x-2
Y) -8x2+20x2-8x
T) If f(x)=4x-2, g(x)=-x2+3, and h(x)=23, what is h(g(f(2)))?
Y) f(x)=4x-1, g(x)=-x2+4, and h(x)=23, what is h(g(f(2)))?
T) 23
Y) 23
T) What is the inverse of f(x)=-∞
Y) How do you prove two functions are inverses of each other?
T) There isn't one.
Y) Plug one into the other. If this equals x, do the same for the other. If this also equals x, they are inverses of each other.
T) Find the inverse(s) of f(x)=√x2+3.
Y) Find the inverse(s) of f(x)=√x2+4.
T) f-1(x)=√x2-3, f-1(x)=-√x2-3
Y) f-1(x)=√x2-4, f-1(x)=-√x2-4
T) How many summaries were completed in unit 1? (correct answer will receive 1000 points.)
Y) What was the exact date that we had the Unit 1 test? Include day of the week. (correct answer will receive 2500 points.)
T) 6
Y) 1/31, Thursday