All categories

3 years ago

At which values of X does the function F(x) have a vertical asymptote? Check all that apply

Mathematics

1 answer:

Archy [21]3 years ago

7 0

Answer:

The values of x are -6 , 0 , 1 ⇒ Answers C , D , E

Step-by-step explanation:

* Let revise how to find the vertical asymptote

- Vertical asymptotes of a rational function f(x)/g(x) can be found by

solving the equation g(x) = 0 ⇒ the denominator of the fraction

- Note: this only applies if the numerator f(x) is not zero for the same

x value

* Lets solve the problem

∵ F(x) = 1/x(x + 6)(x - 1)

∵ The denominator of the fraction is x(x + 6)(x - 1)

- To find the equation of the vertical asymptote Put the

denominator = 0

∴ x(x + 6)(x - 1) = 0

- The denominator has three factors, equate each by 0

∴ x = 0

∴ x + 6 = 0 ⇒ subtract 6 from both sides

∴ x = -6

x - 1 = 0 ⇒ add 1 to both sides

∴ x = 1

∴ From all above there are 3 vertical asymptotes at x = -6 , 0 , 1

* The answers are C, D , E

You might be interested in

Which function is graphed below?

lys-0071 [83]

Answer: The second option, y = 3(1/3)^x

Step-by-step explanation: Input each equation into a graphing calculator (preferably GeoGebra online) and check the answer. I linked the equation, but make sure to check anyway just in case :)

7 0

2 years ago

Which statements about the function are true? Select two

iogann1982 [59]

Answer:

The vertex of the function is at (1,-25)

Step-by-step explanation:

I think your question missed key information, allow me to add in and hope it will fit the orginal one.

Part of the graph of the function f(x) = (x + 4)(x-6) is shown below.

Which statements about the function are true? Select two

options.

The vertex of the function is at (1,-25).

The vertex of the function is at (1,-24).

The graph is increasing only on the interval -4< x < 6.

The graph is positive only on one interval, where x <-4.

The graph is negative on the entire interval

My answer:

Given the factored form of the function:

f(x) = (x + 4)(x-6)

<=> f(x) = $x^{2} - 2x -24$

We will convert to vertex form

<=> f(x) = ( $x^{2} - 2x +1$ ) - 25

<=> f(x) = $(x-1)^{2} -25$

=> the vertex of the function is: (1,-25)

We choose: a. The vertex of the function is at (1,-25)

Let analyse other possible answers:

c. The graph is increasing only on the interval -4< x < 6.

Because the parameter a =1 so the graph open up all over its domain and the vertex is the lowest point.

So the graph is increasing in the domain (1, +∞)

=> C is wrong

d. The graph is positive only on one interval, where x <-4

Wrong, The graph is positive only on one interval, where x > 6

e. The graph is negative on the entire interval

Wrong, The graph is negative only on one interval, where -4< x < 6.

7 0

4 years ago

89. In a drawing, a jar holds the numbers 1 to 8. If you draw three numbers to form a three-digit number (without replacement),

torisob [31]

Answer:

1: D. 1/336

Explanation:

10 x 9 x 8 = 720

There are 720 ways for them to come in first, second and third place.

2. Probability = 1/8 x 1/7 x 1/6 = 1/336

The probability is 1/336 or 0.002976.

7 0

3 years ago

The table below shows all of the possible outcomes for rolling two six sided number cubes what is the probability of rolling an

Vanyuwa [196]

Answer:

The probability of rolling an even number first and an odd number second is $\frac{1}{4}$

Solution:

As two cubes are 6 sided, the total number of possibilities are $(6\times6) = 36$

Now in those possibilities the first number will be even and the second number will be odd. If we check the table, such pairs are,

(2,1), (2,3), (2,5), (4,1), (4,3), (4,5), (6,1), (6,3), (6,5)

So, we can see we have total 9 set with the combination of first number even and second number odd. So, the probability of rolling with this combination will be $\bold\frac{9}{36}=\frac{1}{4}\bold$

6 0

4 years ago

Please answer the question from the attachment.

Allushta [10]

All you have to do is witte the half and if the number ans if the half is not an hole number than you jyst witter the disimal

6 0

3 years ago