Vertical asymptotes are
vertical lines which correspond to the zeroes of the denominator of a
rational function<span>.
(They can also arise in other contexts, such as logarithms, but you'll
almost certainly first encounter asymptotes in the context of rationals.) I'll give you an example:
</span>
This is a rational function.
More to the point, this is a fraction. Can you have a zero in the denominator
of a fraction? No. So if I set the denominator of the above fraction equal
to zero and solve, this will tell me the values that x
cannot be:
x2
– 5x – 6 = 0<span>
</span>(x
– 6)(x + 1) = 0<span>
</span>x
= 6 or –1
So x
cannot be
6 or –1,
because then I'd be dividing by zero.
<span>
<span><span>
<span>
</span></span><span><span /><span>
</span>
</span>
</span></span>
The domain is the set
of all x-values
that I'm allowed to use. The only values that could be disallowed are
those that give me a zero in the denominator. So I'll set the denominator
equal to zero and solve.
<span>x2
+ 2x – 8 = 0</span><span>
</span><span>(x
+ 4)(x – 2) = 0</span><span>
</span><span>x
= –4</span> or <span>x
= 2</span>
Since I can't have a
zero in the denominator, then I can't have <span>x
= –4</span> or <span>x
= 2</span> in the domain.
This tells me that the vertical asymptotes (which tell me where the
graph can <span>not
</span>go) will be at the
values <span>x
= –4</span> or <span>x
= 2</span>.
domain:
<span>
</span><span>vertical
asymptotes: <span>x
= –4</span>,<span>
2</span></span>
<span>
<span>
</span></span>
Answer:
The cell is called the structural and functional unit of life as all living organisms are made up of cells. ... Furthermore, cells provide form and structure, process nutrients and convert it into useable energy. Multicellular organisms have specialized cells that perform specific functions.
Step-by-step explanation:
Answer:
2 hours and 30 minutes
Step-by-step explanation:
Want a little trick to solve problems like these? Use military time
1:45 = 13:45
1345-11:15 = 2:30
Answer:
Y≈4.6
Step-by-step explanation:
Because the hypotenuse is 9rad2 and the angle opposite of it is a 90. You can deduce it is a 90-45-45. From this you can tell the legs are 9. You then do 9 tan 26 to get about 4.4, and after this you subtract it from 9.
1. -8x + y = 8b 2. ÷ by 8
3. -x + y over 8 = b