Domain & Range, Evaluating Functions

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

Given the function f(x) = 30 + 12.5x, what is the domain if x represents the number of people?

Back

The domain is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}.

Front

What does it mean if a function's domain includes negative numbers?

Back

It means that the function can accept negative input values, which may or may not be meaningful in the context of the problem.

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

For the function C = 2h + 15, what is the range if h represents hours rented and Frank has $33?

Back

The range is 0 < y < 33.

Front

How do you evaluate a function at a specific point, such as f(-5)?

Back

Substitute -5 into the function's equation and solve for the output.

Front

What is the output of g(x) = 3x + 1 when x = 2?

Back

g(2) = 3(2) + 1 = 7.

Front

What is a linear function?

Back

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

Front

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

Back

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

Front

What does it mean for a function to be defined for non-negative integers?

Back

It means that the function only accepts whole numbers greater than or equal to zero as input.