Study Flashcards

1
Q

The domain of f+g, f-g, and fg is the

A

Intersection of the domain of f and g

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

The domain of a composite function (f ○ g) is the set of x such that

A

g(x) is defined and is in the domain of f

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

g(x) is defined and is in the domain of f

A

The domain of a composite function (f ○ g) is the set of x such that

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Break down 1/√2x^2+1

A

f(1)(x)=x^2

f(2)(x)=2x

f(3)(x)=+1

f(4)(x)= √x

f(5)(x)=1/x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

f(1)(x)=x^2

f(2)(x)=2x

f(3)(x)=+1

f(4)(x)= √x

f(5)(x)=1/x

A

Break down 1/√2x^2+1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

A function is one-to-one if

A

f(x1)=f(x2) implies x1=x2 for all x, and x2 is in the domain of f.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

f(x1)=f(x2) implies x1=x2 for all x, and x2 is in the domain of f.

A

One-to-one function

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

A function is one-to-one if its graph

A

Passes the horizontal line test

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Passes the horizontal line test

A

One-to-one function

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

How do you algebraically determine one-to-one functions?

A

Set it equal to itself and see if it comes out the same

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Set it equal to itself and see if it comes out the same

A

Algebraically determine one-to-one functions

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Let f be one-to-one. The inverse of f is is the function f^-1 defined by

A

x=f^-1(x) iff y=f(x)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

x=f^-1(x) iff y=f(x)

A

The inverse of f is is the function f^-1 defined by

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

f^-1(f(x))=x for all

A

x in the domain of f

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

f(f^-1(x))=x for all

A

x in the domain of f^-1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

How do you show that functions are inverses?

A

If f(g(x))=x

17
Q

If f(g(x))=x

A

Inverse functions

18
Q

Quadratic function form

A

f(x)=ax^2+bx+c where a,b,c are in R and a≠0

19
Q

f(x)=ax^2+bx+c where a,b,c are in R and a≠0

A

Quadratic function form

20
Q

Standard (vertex) form where (h,k) is vertex

A

a(x-h)^2+k

21
Q

a(x-h)^2+k

A

Standard (vertex) form where (h,k) is vertex

22
Q

The graph of every quadratic function is

A

A parabola

23
Q

A parabola is every

A

Quadratic function

24
Q

(h,k) is absolute global minimum of f if

A

F opens upward

25
Q

(h,k) is absolute global maximum of f if

A

F opens downward

26
Q

Any quadratic can be put in vertex form by

A

Completing the square

27
Q

Name all of these:

n^2, n^3,n^4,n^5

A

Quadratic, cubic, quartic, quintic

28
Q

Quadratic, cubic, quartic, quintic

A

n^2, n^3,n^4,n^5

29
Q

A function is continuous if

A

Its graph has no breaks or holes

30
Q

Its graph has no breaks or holes

A

Continuous function

31
Q

A function is smooth if

A

Its graph has no corners or cusps

32
Q

Its graph has no corners or cusps

A

Smooth function

33
Q

What makes a function not a polynomial

A

Negative exponents and not all real R

34
Q

Negative exponents and not all real R

A

Makes a function not a polynomial

35
Q

A polynomial of degree n has at most

A

n distinct real zeros