Functions Flashcards
What is a function?
An operation that can be performed on a real input to obtain a real output.
In an equation of the form y=f(x); what are the independent and dependent variables?
Independent = x Dependent = y
What is a domain?
Domain is a set of allowed values for the independent variable ie x in y=f(x)
What is the range?
The set of possible values, due to the domain, of the dependent variable ie y in y=f(x)
What is the difference between y=sqrtx and y=-sqrtx?
The former is the positive square root and the latter is the negative square root.
How do we investigate a function’s odd/even - ness?
For a selected real input for the independent variable we observe the changes to the real output dependent variable when we change the sign.
How are even functions identified?
When the output value of the function is indifferent to the change in sign of the input value.
How are odd functions identified?
When the output value changes sign when the input value’s sign is changed.
What is meant by periodicity/ what is a periodic function?
A function (f(t)) is periodic with a period of a number T and can be modelled as f(t + nT), for all integers n.
What are the 2(more added later) steps for Curve Sketching?
- Restrict Domain & Range - Put in asymptotes
2. Find intersections; y=0 x=0
What is Continuity(Continuous function)?
When the line of a graph doesn’t have a rift in it. A discontinuous function is a line of a graph that has a rift in it even though it is still defined for all points on the domain(otherwise it wouldn’t be a function).
What are the 3 basic trig ratios?
Sin=o/h
Cos=a/h
Tan=o/a
What does the sin graph look like? What is it’s period? Is it odd even or neither?
Period 2pi
Odd function
What does a cos graph look like? What is it’s period? Is it an odd or even function or neither?
Period 2pi
Even function
What does a tan graph look like? What is its period? Is it an odd or even function or neither?
Period pi
Odd function
