Domain & Range, Evaluating Functions

Front

What is the definition of 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 definition of 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 can you determine if a relation is a function?

Back

A relation is a function if each input value (x) is associated with exactly one output value (y).

Front

What is the vertical line test?

Back

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

Front

Evaluate f(x) = 3x + 2 for x = 4.

Back

f(4) = 3(4) + 2 = 14.

Front

Evaluate f(x) = x^2 for x = 0.

Back

f(0) = 0^2 = 0.

Front

What is the output of the function f(x) = -x + 5 when x = 3?

Back

f(3) = -3 + 5 = 2.

Front

If f(x) = 2x - 1, what is f(5)?

Back

f(5) = 2(5) - 1 = 9.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of the line represented by the function f(x) = 2x + 3?

Back

The slope of the line is 2.