Download Algebra 2 – PreAP/GT

Algebra 2 – PreAP/GT
Discrete vs Continuous
Name ____________________________________
Discrete Data – data that cannot take on any real value measurement within an interval
Example: the number of pennies in a jar
Continuous Data – data that can take on any real value measurement within an interval
Example: the quantity of water in a glass as the water evaporates
Data is typically considered discrete when you count such as the number of pennies in a jar and
continuous when you measure such as the quantity of water in a glass as the water evaporates.
Continuous Function – a function whose graph is an unbroken line or curve with no gaps or breaks
Discontinuous Function – a function whose graph has one or more jumps, breaks, or holes
Examples:
Discrete
Discrete
Continuous
Continuous
A student group is selling chocolate bars for $2 each. The function f  x   2 x gives the amount of
money collected after selling x chocolate bars. f  x  would be considered a discrete function since
only whole number of chocolate bars can be sold which would result in a graph of separated points
(0, 0), (1, 2), (2, 4), etc. The domain of this function would be the whole numbers and the range of this
function would be zero and the even whole numbers.
A low-flow shower head releases 1.8 gallons of water per minute. The function v  x   1.8x gives the
volume of water released after x minutes. v  x  would be considered a continuous function since you
can run the shower any nonnegative amount of time which would results in a linear function starting at
(0, 0) with a slope of 1.8. Both the domain and range of this function would be all real numbers greater
than or equal to 0.
Identify the following situations as discrete or continuous.
1.
Amanda walks at an average speed of 3.5 miles per hour. The function d  x   3.5x gives the
distance (in miles) Amada walks in x hours.
2.
A token to ride a subway costs $1.35. The function s  x   1.35x gives the cost of riding the
subway x times.
3.
A family has 4 gallons of milk delivered every Thursday. The function m  x   4 x gives the
total amount of milk that is delivered to the family after x weeks.
3
inch in diameter weighs 1.23 pounds per foot. The function x  x   1.23x
4
gives the weight of x feet of steel cable.
4.
Steel cable that is
5.
On a number line, the signed distance from a number a to a number b is given by b  a . The
function d  x  gives the signed distance from 3 to any number x.
6.
Davis is a baseball player and is trying to raise money for his team. He gets pledges of $5 for
each homerun he hits plus fixed pledges of $50. The function a  x   5x  50 gives the amount of
money he will earn for hitting x homeruns.
Classify the following graphs as discrete or continuous.
7.
10.
8.
9.