Functions: Domain, Range, One-to-One and Graph Transformations flashcards

Question 1

What is a relation?

Accepted Answer

A set of ordered pairs.

Question 2

In a relation, what is the set of the first components of the ordered pairs called?

Accepted Answer

The domain.

Question 3

In a relation, what is the set of the second components of the ordered pairs called?

Accepted Answer

The range.

Question 4

What is another name for an input value?

Accepted Answer

The independent variable.

Question 5

What is another name for an output value?

Accepted Answer

The dependent variable.

Question 6

Which letter is an input value often labeled with?

Accepted Answer

The lowercase letter x.

Question 7

Which letter is an output value often labeled with?

Accepted Answer

The lowercase letter y.

Question 8

What is a function?

Accepted Answer

A relation in which each possible input value leads to exactly one output value.

Question 9

In a function, what is the input values' collection called?

Accepted Answer

The domain.

Question 10

In a function, what is the output values' collection called?

Accepted Answer

The range.

Question 11

How is the notation y = f(x) read?

Accepted Answer

y is a function of x.

Question 12

In y = f(x), which variable represents the input value?

Accepted Answer

x.

Question 13

In y = f(x), which expressions represent the output value?

Accepted Answer

y, or f(x).

Question 14

What is a one-to-one function?

Accepted Answer

A function in which each output value corresponds to exactly one input value.

Question 15

What does the vertical line test determine?

Accepted Answer

Whether a graph represents a function.

Question 16

By the vertical line test, when does a graph not define a function?

Accepted Answer

When a vertical line can be drawn that intersects the graph more than once.

Question 17

What does the horizontal line test determine, once a graph is known to be a function?

Accepted Answer

Whether the function is one-to-one.

Question 18

By the horizontal line test, when is a function not one-to-one?

Accepted Answer

When a horizontal line intersects its graph more than once.

Question 19

What does g(x) = f(x) + k do to the graph of f?

Accepted Answer

It shifts the graph vertically by k units.

Question 20

In g(x) = f(x) + k, which way does the graph move when k is positive?

Accepted Answer

Up.

Question 21

In g(x) = f(x) + k, which way does the graph move when k is negative?

Accepted Answer

Down.

Question 22

What does g(x) = f(x − h) do to the graph of f?

Accepted Answer

It shifts the graph horizontally by h units.

Question 23

In g(x) = f(x − h), which way does the graph move when h is positive?

Accepted Answer

Right.

Question 24

In g(x) = f(x − h), which way does the graph move when h is negative?

Accepted Answer

Left.

Question 25

What does g(x) = −f(x) do to the graph of f?

Accepted Answer

It reflects the graph about the x-axis (a vertical reflection).

Question 26

What does g(x) = f(−x) do to the graph of f?

Accepted Answer

It reflects the graph about the y-axis (a horizontal reflection).

Question 27

What does g(x) = a·f(x) with a > 1 do to the graph of f?

Accepted Answer

It stretches the graph vertically.

Question 28

What does g(x) = a·f(x) with 0 < a < 1 do to the graph of f?

Accepted Answer

It compresses the graph vertically.

Question 29

What does g(x) = f(bx) with b > 1 do to the graph of f?

Accepted Answer

It compresses the graph horizontally.

Question 30

What does g(x) = f(bx) with 0 < b < 1 do to the graph of f?

Accepted Answer

It stretches the graph horizontally.

Question 31

In transformations, what kind of change is a change to the output, as in f(x) + k?

Accepted Answer

An outside change.

Question 32

In transformations, what kind of change is a change to the input, as in f(x − h)?

Accepted Answer

An inside change.

Question 33

What is an even function?

Accepted Answer

A function with f(x) = f(−x) for every input x.

Question 34

The graph of an even function is symmetric about which line?

Accepted Answer

The y-axis.

Question 35

What is an odd function?

Accepted Answer

A function with f(x) = −f(−x) for every input x.

Question 36

The graph of an odd function is symmetric about which point?

Accepted Answer

The origin.

Functions: Domain, Range, One-to-One and Graph Transformations flashcards

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Functions: Domain, Range, One-to-One and Graph Transformations flashcards

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How this deck was checked

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