Evaluating Functions

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output value for each input value.

Front

How can you determine if a set of values represents a function?

Back

A set of values represents a function if no two ordered pairs have the same first element (input).

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.

Front

How do you evaluate a function at a specific point?

Back

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

Front

What does g(x) = 2^(x-2) represent?

Back

This represents an exponential function where the base is 2 and the exponent is (x-2).

Front

How do you find f(-5) if f(x) = x + 3?

Back

Substitute -5 into the function: f(-5) = -5 + 3 = -2.

Front

What is the significance of the equation f(x) = 0?

Back

The equation f(x) = 0 is used to find the x-values (roots) where the function intersects the x-axis.

Front

How do you find the value of f(4) for the function f(x) = x^2 - 5x?

Back

Substitute 4 into the function: f(4) = 4^2 - 5(4) = 16 - 20 = -4.

Front

What is the process for determining the domain of a function?

Back

To determine the domain, identify any restrictions on the input values, such as division by zero or square roots of negative numbers.