What is the perpendicular bisector?
Line with a gradient perpendicular to the original line at it’s midpoint.
How do we test if a relationship is a function?
vertical line test and if each image of x produces exactly 1 image of y
Whats the domain of a square root?
x ≥ 0
Whats the range of a square root?
y ≥ 0
How do you solve for an inverse function?
swap all x’s with y’s
What is the relationship of the Domain and Range in inverse functions
They are opposites f(x) domain is f-1(x)’s range and vice versa
What do you need to include when they ask you to SKETCH a graph?
- general shape
- y, x intercepts
- vertexes
What do you need to include when they ask you to DRAW a graph?
- use pencil and ruler drawn to scale
- point plotted accurately
How to write domain for (f +/-/x g)(x)
{x | (domain of f), (domain of g)}
How to write domain for (f/g)(x)
{x | (domain of f), (domain of g)} minus (-) where {x|g(x)≠0}
What is the global maximum and minimum?
the highest and lowest points of the entire function
How to determine the # of turning points with just the formula?
highest power -1
(e.g.) x^2 + x + 1
turning points = 2 - 1 = 1
How to determine a horizontal asymptote?
Think about what would happen if x tends to infinity
How to determine a vertical asymptote?
where is f(x) undefined
How can we determine the domain and range of a composite function?
write out the domain and range for both functions and limit in order. so if (f o g)(x): prioritize limiting g(x) first then f(x).
When does a function not have a inverse?
When it does not pass the horizontal line test.
What is the equation for the axis of symmetry in the standard form quadratic?
x = -b/2a
What is the equation for the vertex form of a quadratic?
y = a(x-h)^2 + k
Vertex form quadratic: how to find y-intercept?
(0, ah^2 + k)
Vertex form quadratic: how to find vertex
(h, k)
What is the equation for the factorized form of a quadratic?
y = a(x-p)(x-q)
Factorized form quadratic: how to find y-intercept
(0, apq)
Factorized form quadratic: how to find axis of symmetry
(p+q)/2
