Relations and Functions_Dec 2

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In mathematical terms, if f is a function, then for every x in the domain, there is a unique f(x).

Front

What is the difference of two functions f(x) and g(x)?

Back

The difference of two functions f(x) and g(x) is given by f(x) - g(x). It represents the value of f(x) minus the value of g(x) for each x in the domain.

Front

Given f(x) = 2x - 1 and g(x) = 4x - 3, find f(x) - g(x).

Back

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

Front

What does the expression 'the difference of n and 9' translate to algebraically?

Back

The expression translates to n - 9.

Front

When f(x) = 9 - 3x and g(x) = 5x - 7, find f(x) + g(x).

Back

f(x) + g(x) = (9 - 3x) + (5x - 7) = 2x + 2.

Front

What is the definition of a relation in mathematics?

Back

A relation is a set of ordered pairs, typically representing a relationship between two sets. For example, the relation {(1,2), (2,3)} relates the first elements to the second.

Front

How can you determine if a relation is a function?

Back

A relation is a function if every input (x-value) corresponds to exactly one output (y-value). This can be checked using the vertical line test on a graph.

Front

Given f(x) = -4x + 4 and g(x) = 2x - 5, find f(x) - g(x).

Back

f(x) - g(x) = (-4x + 4) - (2x - 5) = -6x + 9.

Front

What is the sum of two functions f(x) and g(x)?

Back

The sum of two functions f(x) and g(x) is given by f(x) + g(x). It represents the value of f(x) plus the value of g(x) for each x in the domain.

Front

What is the algebraic expression for 'the product of 3 and x'?

Back

The algebraic expression is 3x.