Chapter 2 Functions and Graphs (Year 2) Flashcards
what is a modulus function?
a function of the type y = |f(x)|
what is the modulus function when f(x) is > or = 0?
when f(x) > or = 0, |f(x)| = f(x)
what is the modulus function when f(x) is < 0?
when f(x) < 0, |f(x)| = -f(x)
what is a mapping?
a function if every input has a distinct output. functions can be one-to-one or many-to-one
what is a domain?
the set of all possible inputs for a mapping
what is a range?
the set of all possible outputs for a mapping
what is a composite function?
two or more functions combined
what does fg(x) mean?
apply g first then apply f
what is the relationship between the functions f(x) and f^-1(x)?
they are inverses of each other
what is the relationship between the graphs of the functions f(x) and f^-1(x)?
they are reflections of each other in the line y=x
what is the domain of f(x) for f^-1(x)?
the domain of f(x) is the range of f^-1(x)
what is the range of f(x) for f^-1(x)?
the range of f(x) is the domain of f^-1(x)
how do you sketch the graph of y = |f(x)|?
- sketch the graph of y = f(x)
- reflect any parts where f(x) < 0 (parts below the x axis) in the x-axis
- delete any parts below the x-axis
how do you sketch the graph of y = f(|x|)
- sketch the graph of y = f(x) for x > or = 0
- reflect this in the y axis
What transformation is the graph of y = f(x) + a?
A translation of the graph y = f(x) by the vector 0/a (0 up/down and a left/right)
What transformation is the graph of y = f(x + a)?
A translation of the graph y = f(x) by the vector -a/0 (-a up/down and 0 left/right)
What transformation is the graph of y = af(x)?
A stretch of the graph y = f(x) by a scale factor of a in the vertical direction
What transformation is the graph of y = f(ax)?
A stretch of the graph y = f(x) by a scale factor of 1/a in the horizontal direction
What transformation is the graph of y = -f(x)?
A reflection of the graph of y = f(x) in the x-axis
What transformation is the graph of y = f(-x)?
A reflection of the graph of y = f(x) in the y-axis
