Linear vs. exponential functions & intersections of graphs
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Transcript of Linear vs. exponential functions & intersections of graphs
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