Evaluate 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

The notation for a function is typically written as f(x), where 'f' is the name of the function and 'x' is the input variable.

Front

How do you find f(-4) for the function f(x) = 2x + 3?

Back

Substitute -4 for x: f(-4) = 2(-4) + 3 = -8 + 3 = -5.

Front

What is the output of f(5) for the function f(x) = 2(x - 7)?

Back

Substitute 5 for x: f(5) = 2(5 - 7) = 2(-2) = -4.

Front

How do you solve for x if f(x) = 2 for the function f(x) = 4x + 2?

Back

Set 4x + 2 = 2, then solve: 4x = 0, so x = 0.

Front

What is the range of the function f(x) = x^2 - 6 when the domain is {-3, 3}?

Back

Calculate f(-3) = 3 and f(3) = 3, so the range is {3}.

Front

What is the domain of the function f(x) = 4 + 2x when the range is {0, 6}?

Back

To find the domain, set 4 + 2x = 0 and 4 + 2x = 6. Solving gives x = -2 and x = 1, so the domain is {-2, 1}.

Front

What is the difference between domain and range?

Back

The domain is the set of all possible input values (x-values) for a function, while the range is the set of all possible output values (y-values).

Front

What is a linear function?

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.