Use the table to work out the values of a, b, c, and d.

*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

Which expression is equivalent to (-2)(a+6)

Eva8 [605]

The equivalent answer to this expression is found by using the distributive property.
(-2a - 12)
Simply multiply the negative 2 into the second parenthesis.

3 0

3 years ago

How to solve derivative of (sin3x)/x using first principle

Leona [35]

$\dfrac{d}{dx}(\dfrac{\sin(3x)}{x})$

First we must apply the Quotient rule that states,

$(\dfrac{f}{g})'=\dfrac{f'g-g'f}{g^2}$

This means that our derivative becomes,

$\dfrac{\dfrac{d}{dx}(\sin(3x))x-\dfrac{d}{dx}(x)\sin(3x)}{x^2}$

Now we need to calculate $\dfrac{d}{dx}(\sin(3x))$ and $\dfrac{d}{dx}(x)$

$\dfrac{d}{dx}(\sin(3x))=\cos(3x)\cdot3$

$\dfrac{d}{dx}(x)=1$

From here the new equation looks like,

$\dfrac{3x\cos(3x)-\sin(3x)}{x^2}$

And that is the final result.

Hope this helps.

r3t40

7 0

2 years ago

Read 2 more answers

Jennifer deposits $1,000 into an account that is compounded monthly for 4 years. The account earns 7% interest. What is the endi

TEA [102]

Answer:

1000( 1 + 7/100)^4 = 1310.79601 which is 1311

7 0

3 years ago

Silvie states that the sum of a rational number and an irrational number is sometimes rational and sometimes irrational. Which s

RideAnS [48]

Answer:

A) Silvie is incorrect; the sum of a rational number and an irrational number is always irrational

Step-by-step explanation:

The concept of adding rational and irrational numbers states that the result will always be irrational.

Take for instance the addition of 4.5 and 3.142857

4.5 is a rational number because it can easily be expressed in fractions while 3.142857 is irrational because it can't be expressed as a simple fraction.

The addition of these two numbers gives 7.642857

7.642857 is an irrational number.

Similarly, any sum of two numbers (rational and irrational) will always result in irrational number.

Hence, Silvie is incorrect.

4 0

3 years ago