Asymptotes
The horizontal asymptote of y = 1/x +3 is y=?
y = 3
TRUE OR FALSE: The graph of y = 1/(x+1) shifts up.
FALSE: shifts left
What x-values would you plug into the equation y = 1/x to get y-values?
x = 1, 2, 3,...
x = -1, -2, -3,...
What is the domain of y = 2/(x+1)-1
All real numbers except -1
The general form for rational functions is:
y = a/(x-h)+k
The vertical asymptote of y = 1/x + 1 is x=?
x = 0
Does the graph of y = -2/(x+1)-2 shift up or down?
Down
What x-values would you plug in to the equation y = 1/(x-1)?
-1, 0, 2, 3
What is the range of y = 2/(x-1)+3?
All real numbers except 3
Visually, what does the graph of a hyperbola have 2 of?
Branches
What is the vertical asymptote of y = 2/(x+4)-1?
x = -4
Does the graph of y = 1/(x-1)-1 shift left or right?
Right
What y-value do you get when you plug x=-3 into y = -1/(x+2)?
y=1
What is the range of y = -3/(x-1)?
All real numbers except 0
When are the branches of a graph in the first and third quadrants?
When a>0
What is the horizontal asymptote of y = -1/(x-2)-2?
y = -2
How does the graph of y = (1/x) + 1 shift from the parent function?
Shift up 1
What happens when you plug an x-value of 1 into y = 2/(x-1)+1?
There is a vertical asymptote at x=1
What is the domain of y = 1/(x-1)+1?
All real numbers except 1
When are the branches of a graph in the second and fourth quadrants?
When a<0
What are the vertical and horizontal asymptotes of y = -1/(x+1)-3?
VA: x = -1
HA: y = -3
How does the graph of y = 1/(x-3)-1 shift from the parent function?
Down 1
Right 3
What x and y-values would create asymptotes when plugged in to y = -1/x + 1?
x=0; y=1
What is the domain and range of y = 2/(x+2)-1?
Domain: All real numbers except -2
Range: All real numbers except -1
Explain why there is an asymptote when x=h
if x=h, then y = a/0 +k, and there cannot be 0 on the bottom of a fraction