Function Fundamentals Essentials
Master key concepts of function notation, domain, range, and the vertical line test.
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Questions Covered in This Set
10 cards to master
What is a function?
A relation where each input corresponds to exactly one output.
What does f(x) represent in function notation?
The output value when x is the input; read as 'f of x'.
What is the domain of a function?
The set of all possible input values (x-values) for which the function is defined.
What is the range of a function?
The set of all possible output values (y-values) the function can produce.
What is the vertical line test?
If any vertical line crosses a graph more than once, the graph does not represent a function.
Why does division by zero restrict the domain?
Division by zero is undefined, so values that make the denominator zero must be excluded from the domain.
What restriction does a square root create for domain?
The expression under the square root must be non-negative (≥ 0).
If f(x) = x² - 4x + 7, what is f(3)?
f(3) = 9 - 12 + 7 = 4
What is the domain of f(x) = 1/(x - 5)?
All real numbers except x = 5, written as (-∞, 5) ∪ (5, ∞).
What is the range of f(x) = x²?
[0, ∞) because squaring any real number gives a non-negative result.
