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 value of x= 22 and y = 7
Answer:
The equation of the line is; y = 0.5·x + 2
Step-by-step explanation:
The points that define the line CD = C(-2, 1) and D(10, 7)
The equation of the line can be presented in the form of the general equation of a straight line, y = m·x + c
Where;
m = The slope of the line =
c = The y-intercept
From the obtained slope, m = 0.5, using point D(10, 7), the equation of the line in point and slope form is therefore;
y - 7 = 0.5·(x - 10)
From the above equation of the line in point and slope form, we get the general form of the equation of the line as follows
y - 7 = 0.5·(x - 10) = 0.5·x - 5
y - 7 = 0.5·x - 5
y = 0.5·x - 5 + 7 = 0.5·x + 2
y = 0.5·x + 2
The equation of the straight line in general is y = 0.5·x + 2.
Answer:
Step-by-step explanation:
Figure out the area of the sponge A= ab Altitude or height given is 1 inch
Base is 3 inches so Area is 3 square inches.
Total area of the design is given as 66 a square inches. Divide total area by area of the sponge to see the minimum applications (assume no overlap)
66÷3 = 22
For the drawing, you need to reproduce the sunburst by drawing the shape of the sponge in a circle filled in and and the rays coming off. Plan ahead.
Save 11 "hits" for the rays, so you have 11 to make the center circle. Start in the middle and work outward.