RELATIONS & FUNCTIONS
what is a relation
a set of ordered pairs
Is {(1, 2), (2, 4), (3, 6)} a function?
Yes, each x-value has only one y-value.
What is the domain of a relation?
The set of all x-values.
What is the range of a relation?
The set of all y-values.
What is f(3) if f(x) = x + 2?
5
what is a function
a relation where each input has an output
Is {(2, 3), (2, 5), (4, 7)} a function?
No, x = 2 has two outputs.
What is the domain of {(–1, 2), (0, 5), (3, 4)}?
{–1, 0, 3}
What is the range of {(1, 4), (2, 4), (3, 4)}?
{4}
What is g(–2) if g(x) = x² − 1?
3
When is a relation NOT a function?
When one x-value is paired with more than one y-value.
is the vertical line test a valid way to find if the inputs and outputs are a function
Yes.
What is the domain of y = 2x + 1?
All real numbers.
What is the range of y = x²?
y ≥ 0
What is h(0) if h(x) = 4x − 7?
–7
What test determines if a graph is a function?
he vertical line test.
Is y = 4 a function?
Is y = 4 a function?
What is the domain of f(x) = 1/x?
All real numbers except 0.
What is the range of y = 5?
{5}
Write y = 3x − 5 in function notation.
f(x) = 3x − 5
Can two different x-values have the same y-value in a function?
Yes.
what is a function
a relation where each input has a output
What is the domain of f(x) = √(x − 4)?
x ≥ 4
What is the range of f(x) = |x|?
y ≥ 0
what is f(x) = –2x + 1 in standard equation form.
y = –2x + 1