Choose one of the factors of 1331x3

*Asymptotes*<br> g(x) =2x+1/x-3 <br><br> Give the domain and x and y intercepts

Nataly [62]

Answer: Assuming the function is $g(x)=\frac{2x+1}{x-3}$ :

The x-intercept is $(\frac{-1}{2},0)$ .

The y-intercept is $(0,\frac{-1}{3})$ .

The horizontal asymptote is $y=2$ .

The vertical asymptote is $x=3$ .

Step-by-step explanation:

I'm going to assume the function is: $g(x)=\frac{2x+1}{x-3}$ and not $g(x)=2x+\frac{1}{x}-3$ .

So we are looking at $g(x)=\frac{2x+1}{x-3}$ .

The x-intercept is when y is 0 (when g(x) is 0).

Replace g(x) with 0.

$0=\frac{2x+1}{x-3}$

A fraction is only 0 when it's numerator is 0. You are really just solving:

$0=2x+1$

Subtract 1 on both sides:

$-1=2x$

Divide both sides by 2:

$\frac{-1}{2}=x$

The x-intercept is $(\frac{-1}{2},0)$ .

The y-intercept is when x is 0.

Replace x with 0.

$g(0)=\frac{2(0)+1}{0-3}$

$y=\frac{2(0)+1}{0-3}$

$y=\frac{0+1}{-3}$

$y=\frac{1}{-3}$

$y=-\frac{1}{3}$ .

The y-intercept is $(0,\frac{-1}{3})$ .

The vertical asymptote is when the denominator is 0 without making the top 0 also.

So the deliminator is 0 when x-3=0.

Solve x-3=0.

Add 3 on both sides:

x=3

Plugging 3 into the top gives 2(3)+1=6+1=7.

So we have a vertical asymptote at x=3.

Now let's look at the horizontal asymptote.

I could tell you if the degrees match that the horizontal asymptote is just the leading coefficient of the top over the leading coefficient of the bottom which means are horizontal asymptote is $y=\frac{2}{1}$ . After simplifying you could just say the horizontal asymptote is $y=2$ .

Or!

I could do some division to make it more clear. The way I'm going to do this certain division is rewriting the top in terms of (x-3).

$y=\frac{2x+1}{x-3}=\frac{2(x-3)+7}{x-3}=\frac{2(x-3)}{x-3}+\frac{7}{x-3}$

$y=2+\frac{7}{x-3}$

So you can think it like this what value will y never be here.

7/(x-3) will never be 0 because 7 will never be 0.

So y will never be 2+0=2.

The horizontal asymptote is y=2.

(Disclaimer: There are some functions that will cross over their horizontal asymptote early on.)

6 0

3 years ago

What steps would you use to plot (−3, −4, 0) in a 3-dimensional coordinate system?

eimsori [14]

Answer:

a. From the origin, move back 3 units and down 4 units

Step-by-step explanation:

Given:

The coordinates of a point in a 3-dimensional space is given as:

(-3, -4, 0)

The value of 'x' = -3

The value of 'y' = -4

The value of 'z' = 0

At the origin, the values of 'x', 'y', and 'z' are each equal to 0.

So, the coordinates of origin is (0, 0, 0). In order to reach the point (-3, -4, 0) from the point (0, 0, 0), we don't move along the z-axis as the 'z' value remains the same. We need to move along the 'x' and 'y' directions only.

Now, 'x' is equal to -3. Negative values of 'x' occur backwards from origin. So, we move back by 3 units. to reach the point (-3, 0).

Now, the value of 'y' is -4. Negative values of 'y' occur below the origin. So, we move down by 4 units to reach the point (-3, -4).

Therefore, the correct option is option (a)

A graph in 2 dimensional is shown in support of the answer.

8 0

4 years ago

Help plzzzz I don't know what to do

elixir [45]

Answer:

it should be 10,000 square meters

Step-by-step explanation:

my mind

6 0

3 years ago

Read 2 more answers

Calculate the distance between the points M=(-1,-1) and P=(2, -8) in the coordinate plane. Give an exact answer (not a decimal a

pantera1 [17]

This is a Pythagorean Theorem problem. 3^2 + 7^2 = 58. C^2 = 58. C = 7.6157 (exact)

There is no exact answer for this. The closest we can get to 58 is 7.6157, which would leave us at 57.9988. So the approximate value is 7.6, but if you need the closest answer, it’s 7.6157.

8 0

2 years ago

Mr. Hartman purchased 2-pounds of beef that cost

elena-14-01-66 [18.8K]

Answer:

$5.60

Step-by-step explanation:

multiply $2.80 by 2

7 0

3 years ago

Read 2 more answers

Choose one of the factors of 1331x3 – 8y3.