Flashcard 3.2 Function Notation and Evaluating Functions (H)

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as a set of ordered pairs, a graph, or an equation.

Front

What does it mean for a relation to be a function?

Back

A relation is a function if no two ordered pairs have the same first element (input) with different second elements (outputs).

Front

Given f(x) = x^2 + 3, what is f(3)?

Back

f(3) = 3^2 + 3 = 9 + 3 = 12.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you evaluate a function at a specific input?

Back

To evaluate a function at a specific input, substitute the input value into the function's equation and simplify.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represent a point in a coordinate system, where 'x' is the first element and 'y' is the second element.

Front

If g(x) = x^2 - 2, what is g(-1)?

Back

g(-1) = (-1)^2 - 2 = 1 - 2 = -1.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the significance of the y-intercept in a function?

Back

The y-intercept is the point where the graph of a function crosses the y-axis, representing the output value when the input is zero.