Pure 2 Flashcards
How to prove by contradiction?
Start by assuming it’s not true. Use steps to lead to something impossible, a contradiction. Conclude the assumption it’s not true is incorrect.
In proofs, how can rational and irrational numbers be differentiated?
Rational numbers can be expressed like b where and b are integers, irrational numbers cannot.
What is Q?
The set of all rational numbers.
What does the modulus of a number do?
Make it not negative
When f(x) >= 0, the modulus of f(x) =
f(x)
When f(x) < 0, the modulus of f(x) =
-f(x)
How to sketch y = modulus(ax+b)?
Sketch y = ax+b, then reflect the part of the graph below the x-axis in the x-axis
What is domain and range?
Domain = all possible inputs, Range = all possible outputs
A mapping is a function if every input has a distinct output, functions can be what or what?
One-to-one or many-to-one
What type of function is fg(x)?
Composite
What is the inverse of f(x)?
f⁻¹(x)
What does y=f(x) look like in relation to y=f⁻¹(x)?
A reflection in the line y=x
How do the domains and ranges of inverse functions relate?
The domain of f(x) is the range of f⁻¹(x). The range of f(x) is the domain of f⁻¹(x).
How to sketch y = modulus(f(x))?
Sketch f(x), reflect any parts under the x-axis in the x-axis, delete all parts under the x-axis
How to sketch y = f(modulus(x))?
Sketch f(x) for x >= 0, reflect this in the y-axis
What does f(x+a) do?
Translation left by a
What does f(x) + a do?
Translation up by a
What does f(-x) do?
Reflect in y-axis
What does -f(x) do?
Reflect in x-axis
What does f(ax) do?
Horizontal stretch of scale factor 1/a
What does af(x) do?
Vertical stretch of scale factor a
Formula for nth term of an arithmetic sequence
Un = a + (n-1)d; a is the first term and d is the common difference
Formula for the sum of the first n terms of an arithmetic sequence
Sn = (n/2)(2a + (n-1)d); a is the first term and d is the common difference
Formula for the nth term of a geometric sequence
Un = ar^(n-1); a is the first term and r is the common ratio