Evaluating Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does it mean to evaluate a function?

Back

To evaluate a function means to find the output value when a specific input value is substituted into the function.

Front

What is the notation for a function?

Back

Functions are typically denoted by letters such as f, g, or h, followed by the input variable in parentheses, e.g., f(x).

Front

How do you find f(2) for the function f(t) = -2t² + 1?

Back

Substitute 2 for t: f(2) = -2(2)² + 1 = -8 + 1 = -7.

Front

For the function f(x) = x + 3, what value of x makes f(x) = -5?

Back

Set the equation: x + 3 = -5. Solving gives x = -8.

Front

What is the output of f(x) = -2x - 12 when x = -5?

Back

Substituting -5 gives f(-5) = -2(-5) - 12 = 10 - 12 = -2.

Front

How do you solve for x in the equation g(x) = 4x - 1 when g(x) = 19?

Back

Set the equation: 4x - 1 = 19. Solving gives 4x = 20, so x = 5.

Front

For the function f(x) = 2x + 2, what value of x makes f(x) = 2?

Back

Set the equation: 2x + 2 = 2. Solving gives 2x = 0, so x = 0.

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.