CONCEPTS EXAMPLES
3.5 Graphing Linear Inequalities in Two
Variables
Step 1 Graph the line that is the boundary of the region.
Make it solid if the inequality is or
because of the equality portion of the symbol.
Make it dashed if the inequality is or
Step 2 Use any point not on the line as a test point.
Substitute for xand yin the inequality. If the
result is true, shade the region of the line
containing the test point. If the result is false,
shade the other region.
6 7.
... Ú
Graph
Graph the line
Make it solid because of the
equality portion of the symbol
Use as a test point.True
Shade the side of the line containing 1 0, 02.0 ... 5
2102 + 0 ...
?
51 0, 0 2
....
2 x+y=5.2 x+y...5.xy0xy(^0) (0, 0)
5
5
2
2 x + y ≤ 5
3.6 Introduction to Functions
Vertical Line Test
If a vertical line intersects a graph in more than one point,
the graph is not the graph of a function.
The domainof a function is the set of numbers that can
replace xin the expression for the function. The rangeis
the set of y-values that result as xis replaced by each
number in the domain.
To find for a specific value of x, replace xby that
value in the expression for the function.
ƒ 1 x 2The graph shown is not the graph of a
function.
Let Find
(a)the domain of ƒ, (b)the range of ƒ,
(c)(a)The domain is
(b)The range is
(c)ƒ 1 - 12 =- 1 - 1 =- 21 - q, q 2.1 - q, q 2.ƒ 1 - 12.ƒ 1 x 2 =x-1.CHAPTER 3 Review Exercises 241
REVIEW EXERCISES
CHAPTER 3
3.1
1.The line graph shows the number, in millions,
of real Christmas trees purchased for the
years 2002 through 2007.
(a)Between which years did the number of
real trees purchased increase?
(b)Between which years did the number of
real trees purchased decrease?
(c)Estimate the number of real trees pur-
chased in 2005 and 2006.
(d)By about how much did the number of
real trees purchased between 2005 and
2006 decrease?'02 '03 '04 '05 '06 '07Trees (in millions)Source: National Christmas Tree Association.035302520YearPurchases of Real Christmas Trees