Precalculus: Functions flashcards

Question 1

What is a relation?

Accepted Answer

A set of ordered pairs

Question 2

What is a function?

Accepted Answer

A relation in which each input gives exactly one output

Question 3

What is the domain of a relation?

Accepted Answer

The set of all possible input values

Question 4

What is a one-to-one function?

Accepted Answer

A function in which each output comes from only one input

Question 5

What does the vertical line test check?

Accepted Answer

Whether a graph is a function: no vertical line may cross it more than once

Question 6

What does the horizontal line test check?

Accepted Answer

Whether a function is one-to-one: no horizontal line may cross its graph more than once

Question 7

What is the form of set-builder notation?

Accepted Answer

{x | statement about x}

Question 8

In interval notation, what does a square bracket mean, and what does a parenthesis mean?

Accepted Answer

A bracket includes the endpoint; a parenthesis excludes it

Question 9

What is a piecewise function?

Accepted Answer

A function whose output is defined by more than one formula

Question 10

When is a function increasing on an open interval?

Accepted Answer

When f(b) > f(a) for any two inputs a and b in the interval with b > a

Question 11

When is a function decreasing on an open interval?

Accepted Answer

When f(b) < f(a) for any two inputs a and b in the interval with b > a

Question 12

How is the composite function (f ∘ g)(x) defined?

Accepted Answer

(f ∘ g)(x) = f(g(x))

Question 13

What is the domain of a composite function f(g(x))?

Accepted Answer

Inputs in the domain of g whose outputs g(x) lie in the domain of f

Question 14

Which way does g(x) = f(x) + k shift the graph of f when k > 0?

Accepted Answer

Up by k

Question 15

Which way does g(x) = f(x − h) shift the graph of f when h > 0?

Accepted Answer

Right by h

Question 16

Across which axis does g(x) = −f(x) reflect the graph of f?

Accepted Answer

The x-axis (a vertical reflection)

Question 17

Across which axis does g(x) = f(−x) reflect the graph of f?

Accepted Answer

The y-axis (a horizontal reflection)

Question 18

What condition does an even function satisfy, and what is its symmetry?

Accepted Answer

f(x) = f(−x); symmetric about the y-axis

Question 19

What condition does an odd function satisfy, and what is its symmetry?

Accepted Answer

f(x) = −f(−x); symmetric about the origin

Question 20

What must be true of a function for it to have an inverse?

Accepted Answer

It has to be one-to-one, so its graph passes the horizontal line test

Question 21

If f^(−1) is the inverse of f, what is f^(−1)(f(x))?

Accepted Answer

x, for every x in the domain of f

Question 22

How is the graph of an inverse function related to the original graph?

Accepted Answer

It is the reflection of the original across the line y = x

Precalculus: Functions flashcards

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