3rd Mid Six Weeks Exam: Inverses and Operations of Functions

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 two functions to be inverses of each other?

Back

Two functions f(x) and g(x) are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Tags

CCSS.HSF-BF.B.4B

Front

How do you find the product of two functions f(x) and g(x)?

Back

The product of two functions is found by multiplying their outputs: (f⋅g)(x) = f(x) * g(x).

Tags

CCSS.HSF-BF.A.1B

Front

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

Back

(f⋅g)(x) = 3x^3 - 14x^2 + 9x - 4.

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

The sum of two functions is found by adding their outputs: (f+g)(x) = f(x) + g(x).

Tags

CCSS.HSF-BF.A.1B

Front

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

Back

(g+f)(-3) = 39.

Tags

CCSS.HSF-BF.A.1B

Front

How do you find the inverse of a set of coordinates?

Back

To find the inverse, switch the x and y values of each coordinate.

Tags

CCSS.HSF-BF.B.4C

Front

What is the inverse of the coordinates (1, 2), (3, 8), (-3, 6)?

Back

The inverse is (2, 1), (8, 3), (6, -3).

Tags

CCSS.HSF-BF.B.4C

Front

What is the definition of inverse functions?

Back

Inverse functions are functions that 'undo' each other, meaning if f(g(x)) = x, then g is the inverse of f.

Tags

CCSS.HSF-BF.B.4A

Front

How can you determine if two functions are inverses?

Back

To determine if two functions are inverses, check if f(g(x)) = x and g(f(x)) = x for all x in their domains.

Tags

CCSS.HSF-BF.B.4B