options: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.)

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
problem_activity: Problem 1
Determine the rate of change in each situation. Then describe the relationship using function language (for example, ____ is a function of ____ because _____.)
a.
{"table": [{"_attributes": {"class": ["table", "table-bordered"], "style": "width: 100%;"}, "tbody": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "_value": "Amt of watermelon in pounds,", "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$x$$"}]}], "td": [{"_attributes": {"style": "text-align: center;"}, "_value": "0"}, {"_attributes": {"style": "text-align: center;"}, "_value": "0.25"}, {"_attributes": {"style": "text-align: center;"}, "_value": "0.5"}, {"_attributes": {"style": "text-align: center;"}, "_value": "1.5"}, {"_attributes": {"style": "text-align: center;"}, "_value": "2"}, {"_attributes": {"style": "text-align: center;"}, "_value": "3"}, {"_attributes": {"style": "text-align: center;"}, "_value": "5"}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "Cost of watermelon in dollars,", "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$y$$"}]}], "td": [{"_attributes": {"style": "text-align: center;"}, "_value": "0"}, {"_attributes": {"style": "text-align: center;"}, "_value": "0.35"}, {"_attributes": {"style": "text-align: center;"}, "_value": "0.70"}, {"_attributes": {"style": "text-align: center;"}, "_value": "2.10"}, {"_attributes": {"style": "text-align: center;"}, "_value": "2.80"}, {"_attributes": {"style": "text-align: center;"}, "_value": "4.20"}, {"_attributes": {"style": "text-align: center;"}, "_value": "7.00"}]}]}]}]}
b.
$${d=25t}$$
, where
$$d$$
is distance in miles and
$$t$$
is time in hours
c.    Giovanni can decorate
$$2$$
cakes,
$$c$$
, every
$$5$$
hours,
$$h$$
.
Problem 2
Determine the starting or initial output value in each situation.
a.
{"table": [{"_attributes": {"align": "Center", "class": ["table", "table-bordered"], "style": "width:80%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "background-color:#eeeeee"}, "strong": [{"_value": "Distance traveled in cab in miles,", "em": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$x$$"}]}]}]}, {"_attributes": {"style": "text-align:center"}, "_value": "0"}, {"_attributes": {"style": "text-align:center"}, "_value": "1"}, {"_attributes": {"style": "text-align:center"}, "_value": "3"}, {"_attributes": {"style": "text-align:center"}, "_value": "4"}]}, {"td": [{"_attributes": {"style": "background-color:#eeeeee"}, "strong": [{"_value": "Cost of cab ride in dollars,", "em": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$y$$"}]}]}]}, {"_attributes": {"style": "text-align:center"}, "_value": "2.50"}, {"_attributes": {"style": "text-align:center"}, "_value": "4.75"}, {"_attributes": {"style": "text-align:center"}, "_value": "9.25"}, {"_attributes": {"style": "text-align:center"}, "_value": "11.50"}]}]}]}]}
b.
{"table": [{"_attributes": {"align": "Center", "class": ["table", "table-bordered"], "style": "width:80%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "background-color:#eeeeee"}, "strong": [{"_value": "Distance traveled in cab in miles,", "em": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$x$$"}]}]}]}, {"_attributes": {"style": "text-align:center"}, "_value": "1"}, {"_attributes": {"style": "text-align:center"}, "_value": "2"}, {"_attributes": {"style": "text-align:center"}, "_value": "4"}, {"_attributes": {"style": "text-align:center"}, "_value": "5"}]}, {"td": [{"_attributes": {"style": "background-color:#eeeeee"}, "strong": [{"_value": "Cost of cab ride in dollars,", "em": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$y$$"}]}]}]}, {"_attributes": {"style": "text-align:center"}, "_value": "4.50"}, {"_attributes": {"style": "text-align:center"}, "_value": "7.00"}, {"_attributes": {"style": "text-align:center"}, "_value": "12.00"}, {"_attributes": {"style": "text-align:center"}, "_value": "14.50"}]}]}]}]}
c.
$${p=16d+20}$$
where
$$p$$
is the total number of pages read in a book and
$$d$$
is the number of days
Problem 3
The function formula below shows the relationship between temperature in degrees Fahrenheit and degrees Celsius. °F is a function of °C.
$${F=\frac{9}{5}C+32}$$
a.   Determine what 28°C is in °F.
b.   Determine what 23°F is in °C.


correct_option_index: 1

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