Untitled Flashcards Set

1.  

What is an asymptote?

an imaginary line that your function never touches

a part of your function

a point on your graph

a type of fruit

2.  

What is the end behavior? (3x7−4)⋅(4x4+3)−4x3−4x−1−4x3−4x−1(3x7−4)⋅(4x4+3)​

x→∞ y→∞x→∞ y→∞ x→−∞ y→∞x→−∞ y→∞

x→∞  y→−∞x→∞  y→−∞ x→−∞ y→∞x→−∞ y→∞

x→∞ y→−∞x→∞ y→−∞ x→−∞ y→−∞x→−∞ y→−∞

x→∞ y→−34x→∞ y→−43​ x→−∞ y→ −34x→−∞ y→ −43​

3.  

Determine the hole(s) for the following function. f(x)=(x+3)(x−5)(x+3)f(x)=(x−5)(x+3)(x+3)​

x = -3

x = 5

x = -3 and x = 5

x = 0

Does Not Exist

4.  

What discontinuities are present?

A hole when x = 2

A vertical asymptote at x = 2

there is no hole or vertical asymptote

A vertical asymptote a x = 2 and hole at x = 1

5.  

A VERTICAL ASYMPTOTE is a discontinuity that is found by setting the _________= to zero and solving for x

Numerator

Denominator

Right side

Left side

6.  

What is the end behavior? (3x8−3x3−4)−4x3−4x−1−4x3−4x−1(3x8−3x3−4)​

x→∞ y→∞x→∞ y→∞ x→−∞ y→∞x→−∞ y→∞

x→∞  y→−∞x→∞  y→−∞ x→−∞ y→∞x→−∞ y→∞

x→∞ y→−∞x→∞ y→−∞ x→−∞ y→−∞x→−∞ y→−∞

x→∞ y→−34x→∞ y→−43​ x→−∞ y→ −34x→−∞ y→ −43​

7.  

Determine the horizontal asymptote(s) for the following function.
f(x)=2x−5x2−1f(x)=x2−12x−5​

y = 2

y = 1

y = -1

y = 0

Does Not Exist

8.  

Determine all removable points of discontinuity (holes), vertical asympotes, and horizontal asympotes for the following function.
f(x)=2x−12x2+5x−3f(x)=2x2+5x−32x−1​

Holes: x = -3
Vertical: x = 1/2
Horizontal: y = 0

Holes: x = 1/2
Vertical: x = -3
Horizontal: y = 0

Holes: Do Not Exist
Vertical: x = 1/2 and x = -4
Horizontal: y = 1

Holes: x = 1/2
Vertical: x = -3
Horizontal: y = 1

Holes: x = -3
Vertical: x = 1/2
Horizontal: Does Not Exist

9.  

How do you find the x-intercept?

replace all x-values with 0

replace the y-value with 0 or make the numerator equal 0

set denominator equal to 0

compare the degrees of the numerator and denominator

10.  

What's the vertical asymptote of the function?

x = 5

x = 0

x =5 , x = -5

x = 25

11.  

The end behavior of a rational function equals zero when:

the degree of the numerator and denominator are equal

the degree of the numerator is less than the degree of the denominator

the degree of the numerator is greater than the degree of the denominator

the numerator equals zero

12.   What is the X-Intercept?

x= 0

x= 4

x= 5

x= -5