Simplifying

<img src="https://tex.z-dn.net/?f=Y%3D%5Cfrac%7B-2%7D%7Bx%7D%2B4" id="TexFormula1" title="Y=\frac{-2}{x}+4" alt="Y=\frac{-2}{x}+

Studentka2010 [4]

Part A: Vertical asymptote is $x=0$

Part B: Domain is $\left(-\infty \:,\:0\right)\cup \left(0,\:\infty \:\right)$

Part C: Horizontal asymptote is $y=4$

Part D: Range is $\left(-\infty \:,\:4\right)\cup \left(4,\:\infty \:\right)$

Explanation:

Part A: We need to determine the vertical asymptote

The vertical asymptote of a function can be determined by equating the denominator equal to zero.

Thus, we have,

$x=0$

Hence, the vertical asymptote is $x=0$

Part B: We need to determine the domain

The domain of the function is the set of all independent x - values for which the function is real and well defined.

Let us take the denominator and equate to zero.

Hence, we have, $x=0$

Therefore, the function is undefined at the point $x=0$

Thus, the domain of the function is $\left(-\infty \:,\:0\right)\cup \left(0,\:\infty \:\right)$

Part C: We need to determine the horizontal asymptote

The horizontal asymptote of the function can be determined by dividing the leading coefficient of the numerator by leading coefficient of the denominator.

Thus, we have, $y=4$

Hence, the horizontal asymptote of the function is $y=4$

Part D: We need to determine the range

The range of the function is the set of all dependent y -values of the function.

In other words, the range of the function can be determined by substituting the values for x.

Thus, we have,

$\left(-\infty \:,\:4\right)\cup \left(4,\:\infty \:\right)$

Therefore, the range of the function is $\left(-\infty \:,\:4\right)\cup \left(4,\:\infty \:\right)$

6 0

3 years ago

Martha states that -6 is a rational number. Which is a correct explanation for this statement ?

viktelen [127]

Martha is indeed right when she states that -6 is a rational number. Just like the name implies, a rational number is a number that can be written as a/b with b not equal to 0. Since -6 can be written as -6/1, and since that is a ratio, that is why -6 is a rational number.

4 0

3 years ago

Solve the equation 8-6z=26

Ne4ueva [31]

8-6z=26

8-8-6z=26-8

-6z=18

divide by -6 for -6z and 18

-6z/-6=18/-6

z=-3

Check answer by using substitution method

8-6(-3)=26

8+18= 26

26=26

Answer is z=-3

7 0

3 years ago

Read 2 more answers

Help please guys is this right?

andrey2020 [161]

Answer: Correct, are you dragging the line across?

3 0

3 years ago

Graph the linear function p(x)=4x .

Law Incorporation [45]

Answer:

Please find attached the required graph

Step-by-step explanation:

The given equation of the linear function is p(x) = 4·x

Comparing the above equation with the general equation for a straight line, y = m·x + c, we have;

The slope, m = 4, and the y-intercept c = 0

Therefore, the graph can be constructed by drawing a straight line passing through the origin which is inclined to the horizontal axis such that the ratio of the vertical distance of a point on the line from the x-axis to the distance of the point from the y-axis is 4 to 1

However, in order to graph the given function, such that the values of the x and y coordinates of the points on the line representing the equation of the graph are clearly defined, we generate a table of values using Microsoft Excel as follows;

x ${}$ p(x)

0 ${}$ 0

1 ${}$ 4

2 ${}$ 8

3 ${}$ 12

4 ${}$ 16

5 ${}$ 20

6 ${}$ 24

7 ${}$ 28

8 ${}$ 32

9 ${}$ 36

10 ${}$ 40

11 ${}$ 44

12 ${}$ 48

13 ${}$ 52

14 ${}$ 56

15 ${}$ 60

16 ${}$ 64

From which the required graph is constructed using the insert function in Microsoft Excel

8 0

3 years ago