Core 3 - Essentail points to remember Flashcards
Which of - One-to-many - Many-to-one - One-to-one Are functions
Many-To-One
One-To-One
Define function
A special “mapping” such that every element of the domain is mapped to exactly one element in the range
How does one make f(x) = sqrt(x) a function
Changing the domain to x >= 0
Inverse functions are reflections of f(x) in what line
The line of y=x
What is the inverse function of e^x
ln(x)
State the growth and decay equations
N = Ae^(kt) and N=Ae^(-kt)
Where A and k are positive numbers
State the consequence of f(x+a)
Horizontal translation of -a
State the consequence of f(x)+a
Vertical translation of a
State the consequence of f(ax)
Horizontal stretch of 1/a
State the consequence of af(x)
Vertical stretch of scale factor a
State the process to sketch a graph for y=|f(x)|
- Sketch the graph f(x)
- Reflect in the x-axis any parts where f(x)
State the process to sketch graph for y=f(|x|)
- Sketch the graph y = f(x) for x >= 0
- reflect this in the y-axis
sec(theta)
1/cos(theta)
cosec(theta)
1/sin(theta)
cot(theta)
1/tan(theta)
sketch sec(theta)
see google lol
Sketch cosec(theta)
see google lol
Sketch cot(theta)
see google lol
State 2 key identities derived from sin^2(x) + cos^2(x) = 1
- 1 + tan^2(x) = sec^2(x)
- 1 + cot^2(x) = cosec^2(x)
State the inverse function of sin and its domain and range
arcsin
domain: -1
State the inverse function of cos and its domain and range
arccos
domain: -1
State the inverse function of tan and its domain and its range
arctan
domain: all real number
range: -pi/2
Give the double angle formula for sin
sin2A = 2sinAcosA
Give the double angle formulae for cos
cos2A = cos^2A - sin^2A = 2cos^2A - 1 = 1 - 2sin^2A
Give the double angle formula for tan
tan2A = (2tanA)/(1 - tan^2A)
How does one write asinx +- bcosx in terms of only sin or cos
Rsin(x +- alpha)
How does one write acosx -+ bsinx in terms of only sin or cos
Rcos(x -+ alpha)
How does one find “R” in context of trig
sqrt(a^2 + b^2)
How does one find alpha in context of trig
a = tan^-1(b/a)
State the quotient rule
dy/dx = (vdu/dx - udv/dx) / (v^2)
State the product rule
dy/dx = udv/dx + vdu/dx
What is the differentiated form of y = e^f(x)
dy/dx = f1(x)*e^f(x)
What is the differentiated form of y = ln(f(x))
dy/dx = f1(x)/f(x)
State the order in which the trig functions are differentiated
sin(x) cos(x) -sin(x) -cos(x) sin(x) so fourth
