Use the graph of y=e^x (next card) to sketch the graph y=e^x-1+3

Logarithmic functions are the inverse of exponential functions.

Natural Exponential Functions:

y = ex

y = ex - 2 (2 tims to the right)

y = ex-2 (2 down)

y = e2x (horizontal stretch 1/2)

y = 2ex (vertical stretch)

y = -ex (reflection on the x-axis)

y = e-x (reflection on the y-axis)

y = eabs(x) (symmetry in the y-axis)

y = lnx (inverse of y = ex)

Natural Exponential Functions

As e becomes greater negatively, the graph moves closer to 0.

Exponential function:

x=a^y

Logarithmic function:

y=log_ax

The asymptote is the vertical or horizontal line that the graph will move close to, but never reach.

In Uganda, the number of breeding females of an endagered population of gorillas is G₀. Biologists predict that the number of breeding females G in n years' time will, if left alone by man, grow according to G=G₀x5^0.07n

If initially 28 breeding females are in the colony, find G₀.

G₀=28

In order to find the inverse of a function, you switch x and y (as shown below):

y=a^x

x=a^y

^{And then solve for y:}

log_ax=y

y=a^x

y=log_ax

Domain: all x

Range: y > -3

Inverse

y=ln(x+3)-1

Domain: x > -3

Range: all y