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3 years ago

Which statement about the end behavior of the logarithmic function f(x) = log(x + 3) – 2 is true?

Mathematics

1 answer:

Nataly [62]3 years ago

6 0

Answer:

Option A is correct.

Step-by-step explanation:

Let us graph the function $f(x) = log(x + 3)-2$ and analyze it.

The graph has one asymptote: the vertical $x=-3$ . With this information, let us analyze each of the options one by one.

Option A: As x decreases, y moves toward the vertical asymptote at x = -3.

This is true because as we move down along the x-axis to the left we meet the vertical asymptote $x=-3$ .

Option B: As x decreases, y moves toward the vertical asymptote at $x=-1$ .

This is incorrect since the vertical asymptote is not located at $x=-1$

Option C: As x increases, y moves toward negative infinity.

No this is incorrect. As x increases, y moves towards positive infinity.

Option D: As x decreases, y moves toward positive infinity.

No this is incorrect. As x decreases, y moves towards negative infinity.

Thus only option A is correct.

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3 years ago

Victor stands 20 meters from a building that is 45 meters tall. He looks up at the roof edge of the building. What is the measur

Gwar [14]

We know that the height of the building is 45m, and the distance between the building and victor is 20m. Since the problem does not state the height of Victor, we can assume that horizontal line of sight of Victor coincides with the base of the building. This gives us a right triangle with angle x and sides 45m and 20m, as you can see in the diagram.

Now, to find the value of the angle x, we will need a trigonometric function that relates the opposite side of our angle x with the adjacent side of it; that trigonometric function is tangent. Remember that $tangent (\alpha) = \frac{oppositeside}{adjacentside}$

We know for our diagram that the opposite side of Victor's angle of inclination, x, is the height of the building (45m), and the adjacent side of it is the distance between Victor and the building (20m). Now we can replace the values in our tangent equation to get:

$tan(x)= \frac{45}{20}$

But we need to find the value of x not the value of tangent, so we are going to use the inverse function of tangent, arctangent (arctan)

$x=arctan( \frac{45}{20} )$ to solve the equation for x:

$x=66$

We can conclude that Victor's angle of inclination from he stands to the top of the building is 66°.

5 0

4 years ago

Let's illustrate the idea of a sampling distribution in the case of a very small sample from a very small population. The given

Olegator [25]

Answer:

a: sample mean: 130.2 pounds

This is not the population mean

Step-by-step explanation:

To find the mean weight of the sample, add up all the values and divide by the total number of values entered. In this case, 10, so we have...

mean: (136 + 99 + 118 + 129 + 125 + 170 + 130 + 128 + 120 + 147)/10 =

1302/10 = 130.2

This is not the population mean. It is the mean of the sample. We would have to know more information to make a conjecture about the population mean.

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3 years ago

X +4 = 12; x = 16 Please help

alexdok [17]

Answer:

x=8 x=16

Step-by-step explanation:

Given function:

x+4=12
x=16

Thinks:

12=4+x
x would be equal to 16

Rewrite as:

x=8 since 8+4=12
x=16=16

Thereform, x=8 and x=16.

3 0

3 years ago

Can you help me with number 10

rewona [7]

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4 years ago