MP3 - Classwork #2

Front

What is the definition of a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Front

What does the notation f(n) represent?

Back

f(n) represents the value of the function f at the input n.

Front

Calculate f(3) for the function f(n) = (n-1)^2 + 3n.

Back

f(3) = (3-1)^2 + 3(3) = 4 + 9 = 13.

Front

What is the significance of the output value in a function?

Back

The output value indicates the result of applying the function to a specific input.

Front

What is the formula for a linear function?

Back

A linear function can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

Given f(x) = 3x - 5, what is f(4)?

Back

f(4) = 3(4) - 5 = 12 - 5 = 7.

Front

What is the meaning of the term 'domain' in relation to functions?

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

If f(x) = (1/2)x^2 - (1/4)x + 3, what is f(8)?

Back

f(8) = (1/2)(8^2) - (1/4)(8) + 3 = 32 - 2 + 3 = 33.

Front

What does it mean for a relation to be a function?

Back

A relation is a function if each input is associated with exactly one output.