Lesson 3 ­ Characteristics of Linear Functions Marked.notebook
Characteristics of a Linear Function
The DOMAIN of any function is the set of all possible input values (x's).
** For linear functions, the domain is ALWAYS
_______________.
(unless a restriction is given)
Ex 1 Find the domain and range of each of the following graphs
a)
b )
The RANGE of any function is the set of all possible output values (y's).
** For linear functions, the range is ALWAYS ______________.
(unless a restriction on the domain is given)
The EXTREMA are the maximums and minimums of a function. Ex 2 Find the extrema of each of the following graphs
a)
b )
The MAXIMUM of a linear function is the greatest y­value represented by some point on the graph The MINIMUM of a linear function is the smallest y­value represented by some point on the graph
The graph of a linear function, and its slope can also help you identify the.....
interval(s) of increase: for what values of x is the "slope" of the graph positive?
Ex 3 Find the intervals of increase/decrease
for each of the following graphs
a)
b )
interval(s) of decrease: for what values of x is the "slope" of the graph negative?
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Lesson 3 ­ Characteristics of Linear Functions Marked.notebook
The End Behavior of a function describes how the ends of the graph "move" as the domain approaches it's minimum and maximum
values
Ex 4 Describe the end behavior for each of the following graphs
a)
b )
y­intercept of a function
x­intercept of a function
The y­intercept of a function is the point at which the graph of the function crosses the
y­axis.
The x­intercept of a function is the point(s)
at which the graph of the function crosses the x­axis.
** Any point (0, b) that is a solution of the equation is the y­intercept ** Any point (a, 0) that is a solution of the equation is an x­intercept
To find graphically: identify the point where the graph crosses the y­axis
To find graphically: identify the point where the graph crosses the x­axis
To find algebraically: plug zero in for x, and solve for y
To find algebraically: plug zero in for y, and solve for x
Ex 5 Determine the following characteristics of the graph:
Ex 6 Determine the following characteristics of the graph:
a) domain
a) domain
b) range
b) range
c) extrema
c) extrema
d) interval of increase/decrease
d) interval of increase/decrease
e) end behavior
e) end behavior
f) y­intercept
f) y­intercept
g) x­intercept
g) x­intercept
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Lesson 3 ­ Characteristics of Linear Functions Marked.notebook
Ex 7 Determine the characteristics of the function:
a) domain
b) range
Ex 8 Determine the characteristics of the function:
a) domain
c) extrema
b) range
d) interval of increase/decrease
c) extrema
e) end behavior
d) interval of increase/decrease
f) y­intercept
e) end behavior
g) x­intercept
f) y­intercept
g) x­intercept
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