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Question 1

A rational function has the form

Answer 1

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

Question 2

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

Answer 2

Rational number form

Question 3

A number is NOT a polynomial when

Answer 3

Negative exponents, variable in denominator, or radicals

Question 4

Negative exponents, variable in denominator, or radicals

Answer 4

Factors that make a number NOT a polynomial

Question 5

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

Answer 5

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

Question 6

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

Answer 6

A hole in the line

Question 7

A hole in a line on a graph appears when

Answer 7

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

Question 8

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

Answer 8

Day 16 page 3

Question 9

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

Answer 9

Lim x — > 0 +

Question 10

Lim x — > 0 +

Answer 10

As x approaches 0, the function gets bigger with bound

Question 11

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

Answer 11

Lim x — > 0 -

Question 12

Lim x — > 0 -

Answer 12

As x approaches 0, the function gets smaller with bound

Question 13

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

Answer 13

Lim f(x) = +- ∞ 
x — > a

Question 14

Lim f(x) = +- ∞ 
x — > a

Answer 14

The line x = a is a vertical asymptote of f

Question 15

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

Answer 15

Lim 1/x = 0

x — > ∞ and x — > -∞

Question 16

Lim 1/x = 0

x — > ∞ and x — > -∞

Answer 16

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

Question 17

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

Answer 17

Lim f(x) = k
x — > +- ∞

Question 18

Lim f(x) = k
x — > +- ∞

Answer 18

The line y=k is a horizontal asymptote of f

Question 19

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

Answer 19

f(x) = 1/x

Question 20

Transformation of 1/x

Answer 20

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

Question 21

What transformations occur in:

g(x) = -2 / x+1

Answer 21

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

Question 22

How do you find the transformations of:

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

Answer 22

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

Question 23

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

Answer 23

D(a) = 0

Question 24

D(a) = 0

Answer 24

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

Question 25

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

Answer 25

x = +- 3

Question 26

How do you find the vertex of a quadratic?

Answer 26

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

Question 27

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

Answer 27

Vertex of a quadratic

Question 28

Axis of symmetry formula

Answer 28

-b / 2a

Question 29

-b / 2a

Answer 29

Axis of symmetry formula

Question 30

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

Answer 30

A hole in the graph at that x value

Question 31

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

Answer 31

y = 0 is a horizontal asymptote

Question 32

y = 0 is a horizontal asymptote of a function when

Answer 32

Degree n < m

Question 33

If n = m, then

Answer 33

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

Question 34

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

Answer 34

If n = m

Question 35

If n > m, then

Answer 35

There is no horizontal asymptote

Question 36

There is no horizontal asymptote when

Answer 36

n > m

Question 37

How is a function odd or even?

Answer 37

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

Question 38

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

Answer 38

Set function equal to horizontal asymptote and solve

Question 39

Set function equal to horizontal asymptote and solve

Answer 39

determine if a graph crosses a horizontal asymptote

Question 40

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

Answer 40

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

Question 41

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

Answer 41

draw a number line of a rational function with vertical asymptotes

Question 42

For slant asymptotes, what do you do?

Answer 42

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.

Question 43

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.

Answer 43

Slant asymptotes

Question 44

How is f(x+h) - f(x) / h where | f(x) = 3-2x^2 written?

Answer 44

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

Question 45

What is the transformation that turns f into g? f(x) = √x g(x) = √x+3

Answer 45

Shift left 3

Question 46

Average rate of change formula

Answer 46

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

Question 47

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

Answer 47

Average rate of change formula

Question 48

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

Answer 48

Odd multiplicity crosses, even touches

Question 49

Wat determines end behavior?

Answer 49

Degree (even or odd) Leading coefficient (pos. or neg.) Direction of x (x—>+∞ or x—>-∞)