Exponential and Logarithmic Functions

Jump discontinuity

Infinite discontinuity

Essential discontinuity

Point discontinuity

Essential discontinuity

Point discontinuity

Infinite discontinuity

Jump discontinuity

A decaying exponential function

A growing exponential function

An oscillating trigonometric function

A linear function with negative slope

Real numbers except multiples of pi.

All real numbers.

Nonpositive real numbers only.

Real numbers except multiples of pi/2.

$(3x)^4$

$4x^3$

$x^{3+4}$

$3x^4$

The rate of increase is proportional to its current value.

The rate of increase remains constant over time.

The rate of decrease is proportional to its current value.

The amount added each time period stays the same.

x = -1

x = -3

x = 3

x = 1

The graph will be linear instead of curved.

The function represents exponential growth.

The base has no effect on the type of change represented by the function.

The function represents exponential decay.

Decay function

Growth function

Constant function

Linear function

$(8)^x$

$5^{3x}$

$(15)^x$

$(5x)^3$