Function Operations Review

Front

What is the definition of a function?

Back

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

Tags

CCSS.8.F.A.1

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it assigns different outputs to different inputs, meaning no two different inputs produce the same output.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse of a function, swap the input and output variables and solve for the new output variable.

Tags

CCSS.HSF-BF.B.4A

Front

What is the formula for the inverse of the function f(x) = 5x + 1?

Back

The inverse is f^{-1}(x) = (x - 1)/5.

Tags

CCSS.HSF-BF.B.4A

Front

What is function addition?

Back

Function addition is the operation of combining two functions, defined as (f + g)(x) = f(x) + g(x).

Tags

CCSS.HSF-BF.A.1B

Front

How do you find (f + g)(x) for f(x) = 5x - 7 and g(x) = 3x + 10?

Back

(f + g)(x) = (5x - 7) + (3x + 10) = 8x + 3.

Tags

CCSS.HSF-BF.A.1B

Front

What is function subtraction?

Back

Function subtraction is the operation of subtracting one function from another, defined as (f - g)(x) = f(x) - g(x).

Tags

CCSS.HSF-BF.A.1B

Front

How do you find (f - g)(x) for f(x) = 5x - 7 and g(x) = 3x + 10?

Back

(f - g)(x) = (5x - 7) - (3x + 10) = 2x - 17.

Tags

CCSS.HSF-BF.A.1B

Front

What is the result of (g - f)(x) for g(x) = 3x + 10 and f(x) = 5x - 7?

Back

(g - f)(x) = (3x + 10) - (5x - 7) = -2x + 17.

Tags

CCSS.HSF-BF.A.1B

Front

What is the significance of 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.

Tags

CCSS.HSF.IF.A.1

CCSS.8.F.A.1