Math Test 5

Front 1

Facts about exponential functions F(x)=a^x

Back 1

a>0, x is a real number.

Front 2

Facts about exponential functions

Back 2

1. Domain is all real numbers
2. The range is (0, infinity).
3. The y-intercept is (0, 1)
4. Y=0 is a horizontal asymptote.
5. f is increasing if a>0.
6. f is decreasing if 0<a<1

Front 3

Exponential functions when is f increasing?

Back 3

F is increasing if a>0

Front 4

Exponential functions when is f decreasing

Back 4

F is decreasing if 0<a<1

Front 5

What is the range of an exponential function?

Back 5

The range is (0, infinity)

Front 6

What is the domain of an exponential function?

Back 6

All real numbers

Front 7

What is the y intercept of an exponential function?

Back 7

(0,1)

Front 8

compound interest formula

Back 8

A=P(1+r/n)^nt

Front 9

Compound interest formula (continuous compounding)

Back 9

A=Pe^rt

Front 10

Logarithmic functions

Back 10

For x>0, a>0, and a does not equal 1, y=log base a x if and only if x=a^y

Front 11

Properties of logarithms

Back 11

1. log base a 1=0 because a ^0=1.
2. log base a a= a^x=1 because a^1=a.
3. logbase a a^x=x and a^logx=x
4. If log base a X-log base a y, then x=y

Front 12

Properties of graphs of logarithmic functions

Back 12

1. the domain is (0, infinity).
2. The range is all real numbers.
3. The x intercept is (1, 0)
4. the y axis is a vertical asymptote.
5. The function is increasing (a>0).

Front 13

Properties of natural logs

Back 13

1. ln 1=0 because e^0=1
2. ln e=1 because e^1=e
3. ln e^x=x and e^ln x= x
4. if ln x = ln y, then x=y.