Exponents
For any number, other than zero, a0 = ?
1
sqrt(81) - sqrt(6) + 4sqrt(6)
9 + 3sqrt(6)
What is the domain? range?
domain: all real numbers
range: (0 , infinity)
What transformation is occurring in: 2x-1
How do you know if something is a function?
vertical line test
How do you get rid of a negative exponent?
Move it from the numerator to denominator or vice versa.
sqrt(5a3b5) * sqrt(125ab3c5)
5a2b4c2*sqrt(c)
Horizontal asymptote?
y = 0
What transformation is occurring: 2x-3
Horizontal transformation to the right 3.
34*32
36
sqrt(26a5) / sqrt(2a2b)
a * sqrt(13a/b)
x-intercept? y-intercept?
no x-intercept
y-intercept is one
What transformation is occurring: (1/5)2x
Vertical compression by 1/5
In order to have an inverse that has no domain restrictions, what must be true about the function?
It must be one-to-one.
56 / 52
54
rationalize (5 + sqrt(3)) / (3 - sqrt(2))
(15 + 5sqrt(2) + 3sqrt(3) + sqrt(6)) / 7
compound interest formula?
y = p ( 1 + r/n)nt
Reflection over the x-axis
How can you check if two functions are inverses?
Composition both ways will result in x:
f(f-1(x)) = x = f-1(f(x))
(73)4
712
5th root of 36
361/5
You start out with $3,000 in your bank account. You earn 5% interest every month. How much, to the nearest cent, do you have after 5 years?
$56,037.56
What transformation is occurring here: 2-x
Reflection over the y-axis
Find the inverse of y = 7x - 5
y = (x+5)/7