Functions Flashcards
What is meant by a “Critical Point”?
Any point on a curve where the slope of the tangent to the curve is zero (parallel to x-axis) OR where the slope of the tangent th the curve is undefined (parallel to Y-axis).
What is meant by a “Stationary point”?
Any point on a curve where the slope of the tangent to the curve is zero (parallel to x-axis)
What is meant by a “local maximum”?
A point on the curve where the function has a greater value at that point than at any points close to it. Not necessarily the greatest value of the function. Can be more then one.
What is meant by a “local minimum”?
A point on the curve where the function has a lesser value at that point than at any points close to it. Not necessarily the least value of the function. Can be more then one.
What is meant by a “global maximum”?
Occurs when f is defined over a domain A: a
What is meant by a continous and discontinous function?
Continous: no break in the curve of the function.Discontinous: Is a break in the function
What is meant by an odd function?
-f(x) = f(-x)
graph is rotational 180º about the origin
EX Sine curve sin(-45) = -sin(45)
What is meant by an even function?
f(-x) = f(x)
graph is symmetrical under reflection in the y-axis.
EX Cosine curve cos(-45) = cos (45)
What is a one-to-one function?
Elememts in the Domain must map to one and only one element in the range.
How do you graphically show if a function is One-to-one?
Take a horizontal line and move it up and down over the graph. If at any point the line crosses the graph at more than one point then the function is NOT one-to-one!
How do you know if a function is an onto function?
A function where the range is equal to the codomain - there are no extra elements in the codomain. (The range is a subset of the codomain)
How do you draw the inverse of a function?
Reflection of the function in the line y=x
When is a function non differentiable?
At corners or discontinous points. Only a continous fn can be differentiable
How do you know if a function has an inverse?
It is a one-to-one fn (one element in the domain mapped to one lement in the range and vice versa!) and an onto fn.
How do you find the inverse of a function?
Ex. f(x) = 3x2 + 5
y = 3x2 + 5
Change the subject to x:
x = [(y-5)/3]1/2
then sway x for y
f-1(x) = [(x-5)/3]1/2
