Domain
Zeros
Transformations
Compositions
Inverse Functions
100
Find the domain of f(x) = 1-2x^2.
What is all real numbers?
100
Find the zeros of f(x) = x/(9x^2 - 4)
What is x = 0?
100
Name the parent function of f(x) = (x -3)^2 + 5
What is f(x) = x^2 or the squared function?
100
Find (f + g)(x) if f(x) = 3x^2 + x and g(x) = 4x - 2.
What is (f + g)(x) = 3x^2 + 5x - 2?
100
Find the inverse function for f(x) = (5 - 3x)/2
What is y = (5 - 2x)/3?
200
Find the domain of f(x) = 3y/(y + 5)
What is y cannot equal -5?
200
Find the zeros of f(x) = the square root of (3x + 2).
What is x = -2/3?
200
Name the parent function of f(x) = -1/(x +3)
What is f(x) = 1/x or the reciprocal function?
200
Find (f-g) (x) if f(x) = x^2 + 2 and g(x) = -4x + 7.
What is (f - g) (x) = x^2 + 4x - 5?
200
Find the inverse function of f(x) = the cubed root of (x + 1)
What is y = x^3 - 1?
300
Find the domain of f(x) = the cubed root of (t + 4)
What is all real numbers?
300
Find the zeros of f (x) = the square root of (2x) - 1
What is x = 1/2?
300
Write the function given that the parent function is f(x) = x^3. It moves 5 units to the left and upwards 4 units.
What is f(x) = (x + 5)^3 + 4?
300
Find (fg)(x) when f(x) = -3x + 2 and g(x) = x^3.
What is (fg)(x) = -3x^4 + 2x^3?
300
Explain how to use the vertical and horizontal line tests.
The vertical line tests whether or not f(x) is a function. If the vertical lines passes through 2 points of the graph, it is not a function. The horizontal line test tests to see if f(x) has inverse function. If the horizontal line passes through 2 points of the graph, then it does not have an inverse.
400
Find the domain of f(x) = 10/(x^2 - 2x)
What is x cannot equal 0 and -2?
400
Find the zeros of f(x) = 1/2x^3 - x
What is x = 0, square root of 2, -square root of 2?
400
Name the function that has a parent function of f(x) = absolute value of x. It moves 3 units to the left, reflects about the x-axis, and shrink it vertically by 1/2.
What is f(x) = -1/2 absolute value of (x + 3)?
400
Find (f/g)(x) if f(x) = x^2 - 4 and g(x) = square root of (x + 2)
What is (f/g)(x) = (x-2)times the square root of (x+2)?
400
Find the inverse of f(x) = (6x + 4)/(4x + 5).
What is y = (5x -4)/6 - 4x)?
500
Find the domain of f(x) = (x -5)/(the square root of (x^2 - 9)
What is x <-3 and x >3?
500
Find of the zero of f(x) = 4x^3 - 24x^2 - x + 6
What is x = 1/2, -1/2, 6?
500
Find the function that has a parent function of f(x) = 1/x. It shifts 2 units to the right, stretches horizontally by 2, and shift it up by 2 units.
What is f(x) = 1/(2x-2) + 2?
500
Find g(f(x)) if f(x) = 3/(x^2 -1) and g(x) = x + 1
What is g(f(x)) = (x^2 + 2)/(x^2 - 1)?
500
Using compositions, show if f(x) and g(x) are inverses of each other. f(x) = (x + 3)/(x - 2) and g(x) = (2x + 3)/(x -1)
What is both f(g(x)) and g(f(x)) are equal to x. (Must see the work!!)
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