Help, I don't understand ASAP NOW

What are the points of discontinutity y=(x-3)/x^2-12x+27

madreJ [45]

Answer:

$(3, -\frac{1}{6})$

Step-by-step explanation:

We can rewrite the equation as

$y = \frac{x - 3}{(x - 3)(x - 9)}$

Notice that we have $x - 3$ in both the numerator and the denominator, so it looks like we can divide it out. However, what if $x - 3$ is $0$ ? Then we would have $y = \frac{0}{0 \times (x - 9)} = \frac{0}{0}$ , which is undefined. So although it looks like the numerator and denominator can be simplified, the resulting function we would get from simplification would not have the same behavior as this one (since such a function would be defined for $x = 3$ , but this one is not).

A point of discontinuity refers to a particular point which is included in the simplified function, but which is not included in the original one. In this case, the point which is not included in the unsimplified function is at $x = 3$ . In the simplified version of the function, if we plug in $x = 3$ , we get

$y = \frac{1}{((3) - 9)} = -\frac{1}{6}$

So the point $(3, -\frac{1}{6})$ is our only point of discontinuity.

It's also important to distinguish between specific points of discontinuity and vertical asymptotes. This function also has a vertical asymptote at $x = 9$ (since it causes the denominator to be 0), but the difference in behavior is that in the case of the asymptote, only the denominator becomes 0 for a specific value of $x$

5 0

2 years ago

Read 2 more answers

What is the maximum height of the apple equation which formula is -16x^2+56x+40

inn [45]

40; base it off of the y-intercept [C]. What is the unit of measurement?

7 0

3 years ago

A 16 ft monument consists of a rectangular prism and a square pyramid, as shown below. If the exposed surfaces of the monument a

icang [17]

Answer and Step-by-step explanation:

The actual answer is 348.

4 rectangles with area 60 each, which, when added together, equals 240.

1 square with area 36.

Each triangle face is 18 each, so 72.

Add those together and the answer is 348 $ft^2$ :).

#teamtrees #PAW (Plant And Water)

4 0

2 years ago

the legs of a right triangle are 4 units and 7 units. What is the length of the hypotenuse? Select one: a. square root 33 units

Mrac [35]

$\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{4^2+7^2}\implies c=\sqrt{65}$