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

Evaluate f(x) = x^2 for f(-8).

Back

f(-8) = (-8)^2 = 64.

Front

What does it mean to evaluate a function?

Back

To evaluate a function means to calculate the output of the function for a given input.

Front

Given f(x) = 3x + 9, find f(-4).

Back

f(-4) = 3(-4) + 9 = -12 + 9 = -3.

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

Given f(x) = -4x - 10 and f(x) = 10, find x.

Back

Set -4x - 10 = 10. Solving gives x = -5.

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

Evaluate r(3) if r(x) = 4x + 4.

Back

r(3) = 4(3) + 4 = 12 + 4 = 16.

Front

If f(x) = \frac{1}{2}(x + 5) - 3, find f(-9).

Back

f(-9) = \frac{1}{2}(-9 + 5) - 3 = \frac{1}{2}(-4) - 3 = -2 - 3 = -5.

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.