Properties of Functions
This is the mathematical definition of a function.
What is a set of ordered pairs for which every x value has only one y value?
This is what occurs when y-values of a function are multiplied by -1 and x-values are unchanged.
What is a reflection across the x-axis?
This is the function that results when the function f(x) = √(x) is vertically translated 5 units up.
What is f(x) = √(x)+5?
This is what occurs when the y-values are multiplied by a constant value greater than 1 but x-values are left unchanged.
What is a vertical stretch?
This type of function occurs when the x and y values are swapped.
What is an inverse function?
This test can be performed to determine if a relation is a function or not.
What is the vertical line test?
This is what occurs when the x-values of a function are multiplied by -1 and the y-values are left unchanged.
What is a reflection across the y-axis?
When the function f(x) = x2 is horizontally translated 4 units to the left, this is the resulting function.
What is f(x)=(x+4)2?
This is what occurs when the x-values are multiplied by a constant value between 0 and 1 but the y-values are left unchanged.
What is a horizontal compression?
The domain of a function becomes this property for its inverse.
What is the range?
This is the domain and range for the square root function.
What is {xER|x≥0} and {yER|≥0}?
When f(x)=x2 is reflected across the y-axis, this is the resulting function.
What is f(x)=x2?
This is the range of the function f(x)=√(x) after it has been vertically translated 6 units down.
What is {y|y≥-6}?
This is the resulting function when f(x) = x2 is vertically translated 3 units up and then vertically compressed by a factor of 1/4.
What is f(x)=0.25x2+3/4?
This is the resulting function when f(x)=(1/x)+6 is inverted.
What is f(x)=1/(x-6)?
This is the domain and range of the function f(x)=x2.
What is {x|xER} and {y|y≥0}?
This is the range of the function f(x)=x2-4 after it has been reflected across the x-axis.
What is {yER|y≤4}?
This is the domain and range of the function f(x)=1/x after it has been horizontally translated 4 units left.
What is {xER|x≠-4} and {y|y≠0}?
This is the resulting function when f(x) = 1/x has been vertically compressed by a factor of 0.5.
What is f(x)=1/(2x)?
This is the resulting range when you take the inverse of f(x)= √(x-2).
What is {y|y≥2}?
This function has vertical and horizontal asymptotes at x=0 and y=0.
What is f(x)=1/x?
This is the domain of the function f(x)=√(x−6) after it has been reflected across the y-axis.
What is x≤ -6?
This is the domain and range of f(x) = √(x) after is has been horizontally translated 3 units right and vertically translated 5 units down.
What is {x|x≥3} and {y|y≥-5}?
This is the resulting function when f(x) = √(x) is horizontally translated 3 units to the left, and is then horizontally stretched by a factor of 0.25.
What is f(x) = √(4x+12)?
What is f(x) = 2√(x+3)?
This is the domain restriction that must be placed on f(x)=(x-4)2+3 in order for its inverse to be a function.
What is {x|x≥4} OR {x|x≤4}?