Functions and Graphs Flashcards
What is a modulus function?
A function of the type y = |f(x)|
It behaves as follows: when f(x) ≥ 0, |f(x)| = f(x); when f(x) < 0, |f(x)| = -f(x)
How do you sketch the graph of y = |ax + b|?
Sketch y = ax + b then reflect the section below the x-axis in the x-axis.
What is a mapping in the context of functions?
A function where every input has a distinct output.
What are the two types of functions based on output?
- One-to-one
- Many-to-one
What does fg(x) mean?
Apply g first, then apply f. fg(x) = f(g(x)).
What is the relationship between functions f(x) and f-1(x)?
They are inverses of each other: ff-1(x) = x and f-1f(x) = x.
How are the graphs of y = f(x) and y = f-1(x) related?
They are reflections of each other in the line y = x.
What is the domain of f(x) in relation to f-1(x)?
The domain of f(x) is the range of f-1(x).
What is the range of f(x) in relation to 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 y = f(x), reflect parts where f(x) < 0 in the x-axis, and delete parts below the x-axis.
How do you sketch the graph of y = f(|x|)?
Sketch y = f(x) for x ≥ 0 and reflect this in the y-axis.
What does f(x + a) represent?
A horizontal translation of -a.
What does f(x) + a represent?
A vertical translation of +a.
What does f(ax) represent?
A horizontal stretch of scale factor a.
What does af(x) represent?
A vertical stretch of scale factor a.
What effect does f(-x) have on the graph of f(x)?
It reflects f(x) in the y-axis.
What effect does -f(x) have on the graph of f(x)?
It reflects f(x) in the x-axis.
