Algebra and Trigonometry: Functions flashcards

Question 1

What is a relation?

Accepted Answer

Any set of ordered pairs.

Question 2

What makes a relation a function?

Accepted Answer

Every input value produces exactly one output value.

Question 3

What is the domain of a relation?

Accepted Answer

The set of every possible input value.

Question 4

What is the range of a relation?

Accepted Answer

The set of output values produced by the inputs.

Question 5

What is another name for the dependent variable?

Accepted Answer

The output variable.

Question 6

What is another name for the independent variable?

Accepted Answer

The input variable.

Question 7

What is a one-to-one function?

Accepted Answer

A function in which each output value comes from one unique input value.

Question 8

Which test checks whether a graph represents a function?

Accepted Answer

The vertical line test: no vertical line meets the graph more than once.

Question 9

Which test checks whether a function is one-to-one?

Accepted Answer

The horizontal line test: no horizontal line meets the graph more than once.

Question 10

In interval notation, what does a square bracket mean?

Accepted Answer

The endpoint is included in the set.

Question 11

In interval notation, what does a parenthesis mean?

Accepted Answer

The endpoint is excluded from the set.

Question 12

What form does set-builder notation take?

Accepted Answer

{x | statement about x}

Question 13

What is a piecewise function?

Accepted Answer

A function whose output is defined by more than one formula.

Question 14

How is the average rate of change of a function between two inputs found?

Accepted Answer

Difference of the two outputs divided by the difference of the two inputs.

Question 15

When is f increasing on an open interval?

Accepted Answer

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

Question 16

When is f decreasing on an open interval?

Accepted Answer

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

Question 17

What are local maxima and minima together called?

Accepted Answer

Local extrema.

Question 18

What is a composite function?

Accepted Answer

A function built by feeding one function's output into another function as its input.

Question 19

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 20

What condition defines an even function?

Accepted Answer

f(x) = f(−x); its graph is symmetric about the y-axis.

Question 21

What condition defines an odd function?

Accepted Answer

f(x) = −f(−x); its graph is symmetric about the origin.

Question 22

What does multiplying a function's output by −1 do to its graph?

Accepted Answer

Reflects it across the x-axis (a vertical reflection).

Question 23

What does multiplying a function's input by −1 do to its graph?

Accepted Answer

Reflects it across the y-axis (a horizontal reflection).

Question 24

Adding a constant to a function's input produces which transformation?

Accepted Answer

A horizontal shift (left or right).

Question 25

Adding a constant to a function's output produces which transformation?

Accepted Answer

A vertical shift (up or down).

Question 26

If g is the inverse of f, what are g(f(x)) and f(g(x))?

Accepted Answer

Both equal x.

Question 27

What property must a function have to possess an inverse?

Accepted Answer

It must be one-to-one.

Question 28

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

Accepted Answer

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

Algebra and Trigonometry: Functions flashcards

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