Evaluating Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input from a set of inputs, known as the domain.

Front

What does it mean to evaluate a function?

Back

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

Front

Given the function f(x) = -x + 2, what is f(0)?

Back

f(0) = 2.

Front

How do you find f(x-1) for the function f(x) = 3x - 2?

Back

Substitute x-1 into the function: f(x-1) = 3(x-1) - 2 = 3x - 3 - 2 = 3x - 5.

Front

What is the value of f(4) for the function f(x) = 4x + 5?

Back

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

Front

If r(x) = 2x, what is r(-2)?

Back

r(-2) = 2(-2) = -4.

Front

For the function f(x) = \frac{3}{2}x + \frac{1}{2}, what is f(5)?

Back

f(5) = \frac{3}{2}(5) + \frac{1}{2} = \frac{15}{2} + \frac{1}{2} = \frac{16}{2} = 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.

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

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.