Function Junction
The set of output values a function can take.
What is the range?
Describe an asymptote.
What is is a line that a graph approaches but never actually touches?
Factor completely: x² + 5x + 6.
What is (x+2)(x+3)?
cos(60°)
What is 1/2?
The people who are often credited with inventing calculus.
Who are Isaac Newton and Gottfried Wilhelm Leibniz
If f(x) = x+5 and g(x) = 2x, what is (g ∘ f)(x)?
What is 2x + 10?
What is the vertex of f(x) = (x^2-2x+1)?
What is (1,0)?
Factor completely: 2x³ - 16x² + 30x.
What is 2x(x-3)(x-5)?
simplify sin(x)/cos(x)
A slope at a point.
What's a derivative?
f(x)=3−5x−2x^2. Evaluate f(-2)
What is 5?
f(x) = √(3x - 5) / (x^2 - 4)
What is x ∈ [5/3, 2) ∪ (2, ∞)?
Solve for x: (2x+3)/(x-1) = 4.
What is x = 7/2?
Evaluate sin^2 (π/101) + cos^2 (π/101)
What is 1?
What is 0?
The graph of a function and its inverse are symmetric about this line.
What is y = x?
f(x) = (x^2 - 4)(x + 3) / (x^2 - 5x + 6)
Determine the intervals where f(x) > 0 (i.e., where the function is positive).
What is f(x) > 0 for x ∈ (-3, -2) ∪ (3, ∞).
Solve for x: x^3 - 6x^2 + 11x - 6 = 0.
What is x = 1, 2, or 3?
Write a formula to relate 3rd quadrant sin values to 1st quadrant sin values.
What is sin(θ) = -sin(θ - π) where theta is in the 3rd quadrant?
What term represents accumulation of a function in calculus?
What is an integral?
Find the inverse of f(x) = (2x^2+1)/5.
f⁻¹(x) = -√((5x - 1)/2)
What are the asymptotes of f(x) = (2x^2 + 3) / (x(x-1)(x+2))?
x = 0, x = 1, x = -2, y = 0
2x^3 - 9x^2 + x + 6 = 0
What is x = -1, 2, or 3?
Expand sin(2x)
What is = 2sin(x)cos(x)?
What is L'Hopital's rule?
It is true that any 0/0 or inf./inf. indeterminate limit case in f(x)/g(x) = f'(x)/g'(x).