Domains
What two things should you always check when finding the domain of a function?
Radicals and denominators
What is the first step when evaluating a piecewise function?
Check which condition applies
Which expression represents the difference quotient?
f(x+h) - f(x) / h
If f(x)=2x+3 and g(x)=x-1, find f(g(x))
2x+1
Find the vertical asymptote of f(x)=3 / x-5
x=5
Find the domain of √x-4
[4, ∞)
The graph of a piecewise function has an open circle at (2, 5) and a closed circle at (2, 1). What is f(2)?
f(2)=1
The difference quotient is used to find what?
Average rate of change
Let f(x)=x2 and g(x)=x+4, find g(f(x))
g(f(x))= x2+4
Find the horizontal asymptote of f(x)= 2x+1 / x-4
y=2
Find the domain of 1 / x2-9
(-∞, -3) U (-3, 3) U (3, ∞)
A piecewise function has: a left-hand limit at 4 and a right-hand limit at 4, but f(2)=6. Is the function continuous at x=2?
No, because the function value does not equal the limit
Evaluate the difference quotient for f(x)=x2
2x+h
Find the inverse of f(x)=4x-7
f-1(x) = x+7 / 4
Determine which point the function has a hole:
f(x) = x2-9 / x-3
hole at (3, 6)
Find the domain of 1 / √2x-8
(4,∞)
What four things are required for a piecewise function to be continuous at x=a?
-left-hand limit exists
-right-hand limit exists
-limits are equal
-limit equals f(a)
Evaluate the difference quotient for f(x)=3x2-5x+2
6x+3h-5
Let f(x)= 1 / x-2 and g(x) = 3x, find f(g(x))
f(g(x)) = 1 / 3x-2
Find all asymptotes of f(x)= 5x / x2-4
vertical asymptote: x=-2, x=2
horizontal asymptote: y=0
Find the domain of √x+2/x-1
[-2, 1) U (1, ∞)
Given f(x) =
3x-1, x < 0
x2+2, x ≥ 0
Find f(-1)
f(-1) = -4
Evaluate the difference quotient for f(x)=2/3x2-1
-4/3x - 2h
Let f(x)= 2x+1 / 3, find f-1(x) and state its domain
f-1(x)= 3x-1 / 2, domain: (-∞, ∞)
Find all asymptotes of x2+1 / x-1
vertical asymptote at: x=1
no H.A., slant asymptote at: y=x+1