Misc Functions
Domain and Range
Transformations
Even and Odd
Compound, Composite and Inverse Functions
100
Sketch the parent function f(x)=x3
See board
100
Find the domain of f(x) = -6abs(x+1).
What is all real numbers.
100
Identify the parent function for
f(x) =-3 [x-2] + 4
What is the step function, or greatest integer function.
100
Fill in the blank:
An even function's graph is symmetric with respect to _________________.
What is the x-axis?
100
For f(x) = 3x2 -7 and g(x) = -x2-4x +5 Find f(g(x)) (without simplifying)
What is 3 (-x2 -4x +5)2 -7 ?
200
Given the piecewise function on the board, find f(-2)
See board
200
Without graphing, find the range of f(x) = 3x2-7
What is ( -7, infinity)
200
Identify the parent function for f(x) = -2 ln(x-4)
What is the natural log, or ln(x)?
200
Fill in the blank:
An odd function's graph is symmetric with respect to the ___________________.
What is the origin?
200
Find (fg)(x)
for f(x) = 1/x and g(x) = 2x
What is 2?
300
What is the "function" of this machine?
What is fax?
300
Find the domain of f(x) = 10 - sqrt(3-x)
What is x less than or equal to 3?
300
What change can you make in the equation to reflect the graph of f(x) = x2 over the x axis?
What is a negative sign in front of x^2?
300
Using algebra, show f(x) = 1/x is an odd function.
What is f(-x) = 1/-x = -f(x)
300
Find the inverse function of f(x) = x3 + 8
What is the cubed root of (x-8)?
400
Name 3 of the 12 basic functions that are always increasing
What is ln(x), x3, x, sqrt(x), ex?
400
Find the domain of (5x+5)/(3x+9).
What is (-inf, -3) U (-3, inf)
400
What changes in the graph of the function occur when the equation is changed from f(x) = x3 to
g(x) = 2(x-4)3 + 5 Name all changes.
What is 1) vertical stretch of 2 2) horizontal shift of 4 3) vertical shift up of 5
400
Determine if the function f(x) = 2x6 + 5x4 - x2 is even, odd or neither.
What is even?
400
Find the inverse function of f(x) = (x2-3)3 + 6
Yikes! I'll write it on the board
500
Without graphing, determine the boundedness of the function f(x) = -sqrt(x-4)
What is bounded above?
500
Find the domain of f(x)=x/(x2+1)
What is all real numbers?
500
Name the new equation for g(x) from the parent function f(x) = abs (x) if it undergoes a shift of 4 up, horizontal shift of 2 to the left and a horizontal stretch of 2.
What is g(x) = abs(1/2x+2) + 4?
500
Determine if the function f(x) = abs(x + 5) is even, odd or neither?
What is neither?
500
Explain how to verify that two functions are inverses of one another using algebra.
What is find the two combinations of composite functions, simplify and check both are equal to x?
f(g(x)) = g(f(x) = x