Study Flashcards

1
Q

A rational function has the form

A

f(x) = N(x)/D(x) where N(x) and D(x) are polynomials

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

f(x) = N(x)/D(x) where N(x) and D(x) are polynomials

A

Rational number form

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

A number is NOT a polynomial when

A

Negative exponents, variable in denominator, or radicals

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

Negative exponents, variable in denominator, or radicals

A

Factors that make a number NOT a polynomial

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

How is the domain of a number with 4 and 2 as its zeros written?

A

(-∞, 2)U(2,4)U(4, ∞) because 3 is still included

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

When a line has an excluded number from the domain, what happens to the graph?

A

A hole in the line

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

A hole in a line on a graph appears when

A

A function has an excluded number from the domain at a certain x

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

How is f(x)=1/x drawn on graph?

A

Day 16 page 3

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

If x > 0, as x gets smaller (close to 0), 1/x gets larger without bound. How is this represented?

A

Lim x — > 0 +

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

Lim x — > 0 +

A

As x approaches 0, the function gets bigger with bound

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

If x < 0, as x gets closer to 0, 1/x gets smaller without bound. How is this represented?

A

Lim x — > 0 -

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

Lim x — > 0 -

A

As x approaches 0, the function gets smaller with bound

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

The line x = a is a vertical asymptote of f if

A
Lim f(x) = +- ∞ 
x — > a
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q
Lim f(x) = +- ∞ 
x — > a
A

The line x = a is a vertical asymptote of f

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

As x gets larger (x > 0), or farther from 0, 1/x gets smaller approaching 0. How is this represented?

A

Lim 1/x = 0

x — > ∞ and x — > -∞

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

Lim 1/x = 0

x — > ∞ and x — > -∞

A

As x gets larger (x > 0), or farther from 0, 1/x gets smaller approaching 0.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

The line y=k is a horizontal asymptote of f if

A
Lim f(x) = k
x — > +- ∞
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q
Lim f(x) = k
x — > +- ∞
A

The line y=k is a horizontal asymptote of f

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

The function g(x) = ax + b/ cx +d is a transformation of

A

f(x) = 1/x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

Transformation of 1/x

A

g(x) = ax + b/ cx +d

21
Q

What transformations occur in:

g(x) = -2 / x+1

A

Reflection over x-axis, shift left 1, stretch vertical 2

22
Q

How do you find the transformations of:

h(x) = 3x-2 / x-1

A

Use long division. The quotient is added and the remainder is the numerator

23
Q

If f(x) = N(x) / D(x) where N(x) and D(x) have no common factors, then x=a is a vertical asymptote of f iff

A

D(a) = 0

24
Q

D(a) = 0

A

If f(x) = N(x) / D(x) where N(x) and D(x) have no common factors, then x=a is a vertical asymptote of f

25
Q

What are the vertical asymptotes of g(x) = 1 / x^2 -9?

A

x = +- 3

26
Q

How do you find the vertex of a quadratic?

A

(-b / 2a, f(-b / 2a))

27
Q

(-b / 2a, f(-b / 2a))

A

Vertex of a quadratic

28
Q

Axis of symmetry formula

A

-b / 2a

29
Q

-b / 2a

A

Axis of symmetry formula

30
Q

What happens if the x-intercept is not in the domain?

A

A hole in the graph at that x value

31
Q

If f(x) = N(x) / D(x), and degree n < m, then

A

y = 0 is a horizontal asymptote

32
Q

y = 0 is a horizontal asymptote of a function when

A

Degree n < m

33
Q

If n = m, then

A

y = a / b. You divide leading coefficients and get the number

34
Q

y = a / b. You divide leading coefficients and get the number

A

If n = m

35
Q

If n > m, then

A

There is no horizontal asymptote

36
Q

There is no horizontal asymptote when

A

n > m

37
Q

How is a function odd or even?

A

Even when f(-x)=f(x)

Odd when f(-x)=-f(x)

38
Q

How do you determine if a graph crosses a horizontal asymptote?

A

Set function equal to horizontal asymptote and solve

39
Q

Set function equal to horizontal asymptote and solve

A

determine if a graph crosses a horizontal asymptote

40
Q

How do you draw a number line of a rational function with vertical asymptotes?

A

Plot vertical asymptotes and input a number into x above and below horizontal asymptote . Greater than is plus and less than is minus

41
Q

Plot vertical asymptotes and input a number into x above and below horizontal asymptote . Greater than is plus and less than is minus

A

draw a number line of a rational function with vertical asymptotes

42
Q

For slant asymptotes, what do you do?

A

Divide the rational function. The remainder is put over the divisor, and f(x) is above and below the slant asymptote when this is greater than or less than 0.

43
Q

Divide the rational function. The remainder is put over the divisor, and f(x) is above and below the slant asymptote when this is greater than or less than 0.

A

Slant asymptotes

44
Q

How is f(x+h) - f(x) / h where

f(x) = 3-2x^2 written?

A

3-2(x+h)^2 - (3-2x^2) / h

45
Q

What is the transformation that turns f into g?

f(x) = √x g(x) = √x+3

A

Shift left 3

46
Q

Average rate of change formula

A

f(b)-f(a) / b-a

47
Q

f(b)-f(a) / b-a

A

Average rate of change formula

48
Q

How do you determine if a function touches or crosses the x-axis?

A

Odd multiplicity crosses, even touches

49
Q

Wat determines end behavior?

A

Degree (even or odd)

Leading coefficient (pos. or neg.)

Direction of x (x—>+∞ or x—>-∞)