Ch. 7 - Functions Flashcards Preview

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Flashcards in Ch. 7 - Functions Deck (15)
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1
Q

Even Function

A

A function of which ƒ(x) = ƒ(-x).

Even functions are symetrical across the y-axis.

2
Q

Odd Function

A

A function for which -ƒ(x) = ƒ(-x)

Odd functions have origin symmetry, which means that they are the same when reflected across the origin.

3
Q

Root

A

Values in a function’s domain at which the function eqauls zero.

A root is also called a zero, solution, or x-intercept of a function.

4
Q

Frequency

A

The number of times a graph repeats itself in a given distance;

the reciprical of the function’s period

5
Q

Inverse Functions

A

An inverse function always deso the opposite of each opperation in the original function, in reverse order.

6
Q

Inverse Compound Functions

A

If ƒ(g(x)) = x,

then g(x) = ƒ-1(x).

7
Q

Mathematical Impossibilites for Domain

A
  • A fraction havinga denominator of zero.
  • Any even-numbered root of a negative number.
8
Q

Rules that limit a function’s range

A
  • An even exponent produces only nonnegative numbers.
  • The even-numbered root of a quanitity represents only the positive root.
  • Absolute values produce only nonnegative values.

A nonnegative operation has a range of {ƒ(x) ≥ 0}. When an opperation is applied to the function (i.e. * -1, + c, * a), the range is also effected in the same way.

9
Q

To estimate range and domain based on a function’s graph, use these rules…

A
10
Q

Periodic Function

A

A function that repeats a pettern of range values forever.

11
Q

Movement of a function

A
12
Q

Algebraic meaning of the degree of a function

A

It equals the maximum munber of roots that a function has.

13
Q

What is the degree of the term:

3xy2

A

The degree of that term is 3

The degree of a term in a polynomial is the sum of the exponents of the variables in that term.

14
Q

How distinct roots does the following have?

ƒ(x) = x6

g(x) = (x–1)(x–2)(x–3)(x–4)(x–5)(x–6)

A

ƒ(x) has one distinct root.

g(x) has six distinct roots.

15
Q

An nth-degree function has a maximum of n distinct roots and a maximum of (n – 1) local extreme values.

A