5.2: Evaluating Functions (Function Rules)

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 f(x) represent in a function?

Back

f(x) represents the output of the function f for a given input x.

Front

How do you evaluate a function at a specific point?

Back

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

Front

Evaluate f(x) = 4x + 5 at x = 4.

Back

f(4) = 4(4) + 5 = 16 + 5 = 21.

Front

Evaluate f(x) = 3x² - 11 at x = -5.

Back

f(-5) = 3(-5)² - 11 = 3(25) - 11 = 75 - 11 = 64.

Front

Evaluate g(x) = 5 - 6x at x = -5.

Back

g(-5) = 5 - 6(-5) = 5 + 30 = 35.

Front

Evaluate h(x) = x² + 3x at x = -3.

Back

h(-3) = (-3)² + 3(-3) = 9 - 9 = 0.

Front

What is the process to find the x-value when f(x) = k?

Back

Set the function equal to k and solve for x.

Front

For which value of x does f(x) = x + 3 equal -5?

Back

Set x + 3 = -5, then x = -8.

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.