Function or Not?
What is the definition of a function?
Your answer should have the following:
A function is a relation:
where no input has two different outputs
-2 < x ≤ 1
If f(x) = 2x and g(x) = x + 1, what is f(x)*g(x)
2x2 + 2x
If f(x) = 4x and g(x) = 2x, what is f(g(2a))
f(g(x)) = 4g(x) = 4(2x) = 8x
What did Dr. Sam get her Graduate Degree in?
Law!
Is x = y2 a function if x is our set of inputs and y is our set of outputs?
Nope! For example, the input x = 4 can map to either y = -2 or y = 2
What is the domain and range of y = abs(x) ?
Domain: (-oo, oo)
Range: [0, oo)
If f(x) = x +1 and g(x) = x -1, what is f(x)*g(x)
f(x)*g(x)=x2-1
If f(x) = x2 and g(x) = x +2, what is f(g(x))
f(g(x)) = (x+2)2
What two states did Ms. Landis grow up in?
Hawaii and Alaska
Is x = y2 a function if x is our set of outputs and y is our set of inputs?
Yes! Each y value maps to only one input
What is the domain and range of x = y2
All real numbers for both!
2
If f(x) = 2 and g(x) = 2x, what is g(f(3))
g(f(x)) = 2f(3)=22 = 4
Which two City Teachers attended the same College?
Mr. A and Mr. Bond
Yes! Multiple inputs can have a single output without breaking the rules.
Daily double:
What is the domain and range of y = sqrt(x) ?
Domain: [0, oo)
Range: [0, oo)
If f(x) times g(x) is equal to x2 + 5x + 4, what are f(x) and g(x) separately?
f(x) = x + 4 and g(x) = x + 1, or vice versa
If f(x) = (1/x) and g(x)= sqrt(x+1), what is the value of g(f(x))?
1 /sqrt(x+1)
This city teacher grew up in Ohio.
Mr. Deng
A function is made up of two separate pieces: the domain of the first is (-oo, -1) and the second piece is [-1, oo). Could this be a function?
Yes! The input -1 only appears once since -1 isn't in the domain of the first.
What is the domain and range of (1/x)2
Domain: The value of 0 creates a zero by division error, but everything else works.The square prevents us from having negative values and 0 is never an output.
Domain: All real numbers except 0
Range: (0, oo)
f(x) = 1 + x + x2 + ... + xn
g(x) = 1 + x + x2 + ... + xn + xn+1.
What is the value of f(x) - g(x)
xn-1
If f(x) = sqrt(x) and g(x) = x2, is -1 a valid input for g(f(x))?
What book did Mr. Nardie do his college thesis on?
Dracula