Add and subtract 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 add functions?

Back

Adding functions involves combining two functions by adding their outputs for each input. If f(x) and g(x) are two functions, then (f + g)(x) = f(x) + g(x).

Front

What does it mean to subtract functions?

Back

Subtracting functions involves combining two functions by subtracting the output of one from the other. If f(x) and g(x) are two functions, then (f - g)(x) = f(x) - g(x).

Front

If f(x) = 2x + 3 and g(x) = x - 1, what is (f + g)(x)?

Back

(f + g)(x) = (2x + 3) + (x - 1) = 3x + 2.

Front

If f(x) = 2x + 3 and g(x) = x - 1, what is (f - g)(x)?

Back

(f - g)(x) = (2x + 3) - (x - 1) = x + 4.

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 find the composite of two functions?

Back

The composite of two functions f and g, denoted as (f ∘ g)(x), is found by substituting g(x) into f. That is, (f ∘ g)(x) = f(g(x)).

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If a vertical line intersects the curve at more than one point, it is not a function.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.