Function Notation and Evaluating Functions

Front

What is function notation?

Back

Function notation is a way to represent a function using symbols, typically written as f(x), where 'f' is the name of the function and 'x' is the input variable.

Front

How do you evaluate a function at a specific value?

Back

To evaluate a function at a specific value, substitute the value into the function's equation in place of the variable.

Front

Evaluate h(x) = -x² + 3x for h(-3).

Back

h(-3) = -(-3)² + 3(-3) = -9 - 9 = -18.

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

Evaluate f(x) = -2x + 13 for f(-4).

Back

f(-4) = -2(-4) + 13 = 8 + 13 = 21.

Front

What is the output of a function?

Back

The output of a function is the value that results from substituting an input into the function's equation.

Front

Evaluate f(x) = x² for f(-8).

Back

f(-8) = (-8)² = 64.

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

Evaluate f(5) if f(x) = 2x + 6.

Back

f(5) = 2(5) + 6 = 10 + 6 = 16.

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.