Asymptotes
Asymptotes
Continuity
Limits
Discontinuities
100
A vertical line that a function approaches but never reaches
What is a vertical asymptote?
100
Name two continuous functions
Some correct answers: power functions, exponential functions, logarithmic functions
100
What is the limit as x approaches 5 of (x3-2x)?
What is 115?
100
What is the discontinuity in this graph?
What is an asymptote?
200
This graph describes an asymptote at...
What is y=0?
200
What is the interval at which this function is continuous?
What is {x|x ≠ -4}?
200
What is the limit as x approaches 0 of 3/(4+2x)1/2?
What is 3/2?
200
What discontinuity does f(x) = (x-3)/2x-6 have?
What is a hole?
300
y=lnx has an asymptote. Where?
x=0
300
Under what interval is this function continuous?
What is (-3,8].
300
What is the limit as x approaches -2- of 1/(x+2)?
What is negative infinity?
300
What discontinuity does this function have?
What is a jump?
400
Find the vertical asymptotes for g(x) = 8x/(x-3)
What is x=3?
400
Find number k so that f is continuous at every point.
f(x) = x2, if x is less than or equal to 5
f(x) = x+ k, if x is greater than 5
What is k=20?
400
What is the limit as x approaches 4+ of 3/(x2-16)?
What is positive infinity?
400
How many discontinuities does this function have, and what are they called?
4: two jumps, one hole, and one asymptote
500
Find the vertical asymptotes for f(x) = (x-6)/(-x3+36x)
x=0 and x=-6
500
Check whether there is a solution to the equation x5-2x3-2=0 between the interval [0,2].
What is, by IVT, there is a solution?
500
The inequality 1 - x < sinx/x < 1 holds when x is measured in radians and |x|<1. Find the limit as x approaches 0 of sinx/x, if it exists.
What is 1?
500
Write the equation/the point for each discontinuity present.
Jump: (-7,4)
Hole: (-3,-2)
Jump: (2,1)
Asymptote: x=4