Key Features Exponential

f(x)=5(.5)^x

f(x)=5(.25)^x

f(x)=10(5)^x

f(x)=10(.75)^x

SLOPE

RATE OF CHANGE

Y-INTERCEPT

GROWTH FACTOR

Exponential Growth

Exponential Decay

Linear

None

y = 6

(0, -4)

y > -6

y < -6

The function represents exponential growth

The y-intercept is  $$\left(0,\ 2\right)$$  

The horizontal asymptote is y = 0 

The domain is all real numbers  $$\left(-\infty,\ \infty\right)$$  

The range is all real numbers  $$\left(-\infty,\ \infty\right)$$  

The domain is  $$\left(-\infty,\infty\right)$$  

The y-intercept is  $$\left(0,-1\right)$$  

The range is  $$\left(-\infty,\infty\right)$$  

As  $$x\rightarrow-\infty,\ f\left(x\right)\rightarrow-4$$   

The function is never decreasing.

exponential growth

exponential decay

a rational function

greater than 1

less than 1

equal to 1

x-intercept: 0 y-intercept: 1 Horizontal Asymptote at the x-axis

x-intercept: none y-intercept: 4 Horizontal Asymptote at the x-axis

x-intercept: 0 y-intercept: 1 Vertical Asymptote at the y-axis

y = 2^x+3

y = 2^x + 3

y = 2^x

y = 2^-x