8.4 Day 1

What is the definition of an ASYMPTOTE?

• A curved line. 
• A line that only touches the origin. 
• A line that only lives on the first quadrant. 
• A line that a curve approaches, as it heads towards infinity. 

The equation of a vertical asymptote is written in the form:

• x=

• y=

• none of the above

Which of the following is determined by just looking at the denominator?

• vertical asymptote
• horizontal asymptote
• holes
• slant asymptote

Does this function have any vertical asymptotes? If so, what are their equations? $y=\frac{\left(x+3\right)\left(x-4\right)\left(x+7\right)}{\left(x-4\right)}$   

• No vertical asymptotes.

• One vertical asymptote: x = 4

• Two vertical asymptotes: x = -3 and x = -7

• Three vertical asymptotes:  x = -3, x = 4, and x = -7

The holes of a rational function occur when :

• my pencil pokes a hole in the paper I'm working on
• there is something left in the denominator
• the value of f(0)
• a factor in the denominator cancels with a factor in the numerator

What is the x-value of the hole? $g\left(x\right)=\frac{\left(x-2\right)\left(x+6\right)}{\left(x+2\right)\left(x-2\right)}$  

• 2

• -2

• -6

• 6

When finding the Horizontal asymptotes of a function, you should be thinking...

• "Set Bottom = to Zero"
• "Top = 0"
• "f(0)"
• "Look at the Degree of the top and bottom..."

What's the horizontal asymptote of the function?

• y = 0

• No horizontal asymptote

• y = 1

• y = 9

Find the horizontal asymptote.

• $y=-2$

• none

• $y=0$

• $y=\frac{1}{2}$

What is the equation of the horizontal asymptote of the given function?

• y = 2

• x = -2

• There isn't one

• y = 5