LINEAR VS. EXPONENTIAL FUNCTIONS&

INTERSECTIONS OF GRAPHS

Holt McDougal Algebra 1

Exponential Functions

The table and the graph show an insect population that increases over time.

Holt McDougal Algebra 1

Exponential Functions

A function rule that describes the pattern above is f(x) = 2(3)x. This type of function, in which the independent variable appears in an exponent, is an exponential function. Notice that 2 is the starting population and 3 is the amount by which the population is multiplied each day.

Holt McDougal Algebra 1

Exponential FunctionsRemember that linear functions have constant first differences. Exponential functions do not have constant differences, but they do have constant ratios.

As the x-values increase by a constant amount, the y-values are multiplied by a constant amount. This amount is the constant ratio and is the value of b in f(x) = abx.

Linear, Exponential, or

Neither

For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer.#1.

Linear

For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer.#2.

Rounds of Tennis

1 2 3 4 5

Number of Players left in Tournament

64 32 16 8 4

Exponential

For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer.

#3. This function is decreasing at a constant rate.

Linear

For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer.

#4. A person’s height as a function of a person’s age (from age 0 to100).

Neither

For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer.#5.

Linear

For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer.

#6. Each term in a sequence is exactly 1/3 of the previous term.

Exponential

INTERSECTIONS OF GRAPHS

Points of Intersection