Graph the function x + y = 6; domain -2,0,4,6

y-intercept

→

(

x

,

y

)

=

(

0

,

4

)

No x-intercept

domain

.

→

{

x

:

x

∈

(

−

∞

,

+

∞

)

}

range

→

{

y

:

y

∈

(

+

3

,

+

∞

)

}

Explanation:

Set

y

=

6

x

+

3

Determine the y-intercept

Set

x

=

0

giving

y

=

6

0

+

3

=

4

Determine the x-intercept

Set

y

=

0

=

6

x

+

3

6

x

=

−

3

Take logs of both sides

x

ln

(

6

)

=

ln

(

−

3

)

But ln(-3) is undefined thus there is no x-intercept

Determine end behaviour

x

→

−

∞

lim

x

→

−

∞

6

x

+

3

=

lim

z

→

+

∞

1

6

z

+

3

→

k

=

3

Determine end behaviour

x

→

+

∞

lim

x

→

+

∞

6

x

+

3

→

k

+

3

=

∞

+

3

=

∞