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3 years ago

How does the graph of g(x)=-(x+3)^4 compare to the parent function of f(x)= x^4

Mathematics

1 answer:

Murrr4er [49]3 years ago

6 0

Answer:

g(x) is flipped across the x-axis and translated -3 units

Step-by-step explanation:

BACKGROUND:

The rules of functions of the type you're asking for follow this structure (note that terms I use may not abide by the textbook definition):

f(x) = a(x - b)^n + c

a - vertical stretch or compression. If negative it will also flip the function across the x-axis.

b - horizontal translation. Note that if the number representing b is positive, there will be a negative translation and if negative there will be a positive translation.

ex: (x + 3) will move the function 3 units to the left or in the negative direction on the graph

c - vertical translation of the function. Does not abide by the same rule as the horizontal in terms of having the opposite effect on the graph compared to what's implied.

ex: (x + 3) - 4 will move 4 units down just like what's implied by the negative sign

n - there are a few special rules you can use to figure out the end behavior (EB) of functions like this one. If the exponent is positive, no matter how big the number it will have the same end behavior as a quadratic function. A function with an odd exponent will have the same end behavior as a linear function. (not useful in this case but still noteworthy)

ex: f(x) = x^2 has the same end behavior as g(x) = x^6

WORK:

In this case, if abiding by these rules, g(x) = -(x + 3)^4 is:

flipped across the x axis because of the negative value for a.
translated 3 units to the left because of the value of b.
has the same end behavior as the function f(x) = -x^2 (EB isn't useful in this case but may be in the future.)

Note: please comment with questions because the explanation I'm giving is highly visual and based on what I was taught, so I'm not a master at this type of math either. I'd recommend the free app Desmos to check out how changing a function impacts its graph.

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Alice searches for her term paper in her filing cabinet, which has several drawers. She knows thatshe left her term paper in dra

katen-ka-za [31]

You made a mistake with the probability $p_{j}$ , which should be $p_{i}$ in the last expression, so to be clear I will state the expression again.

So we want to solve the following:

Conditioned on this event, show that the probability that her paper is in drawer $j$ , is given by:

(1) $\frac{p_{j} }{1-d_{i}p_{i} } , if j \neq i,$ and

(2) $\frac{p_{i} (1-d_{i} )}{1-d_{i}p_{i} } , if j = i.$

so we can say:

$A$ is the event that you search drawer $i$ and find nothing,

$B$ is the event that you search drawer $i$ and find the paper,

$C_{k}$ is the event that the paper is in drawer $k, k = 1, ..., n.$

this gives us:

$P(B) = P(B \cap C_{i} ) = P(C_{i})P(B | C_{i} ) = d_{i} p_{i}$

$P(A) = 1 - P(B) = 1 - d_{i} p_{i}$

Solution to Part (1):

if $j \neq i$ , then $P(A \cap C_{j} ) = P(C_{j} )$ ,

this means that

$P(C_{j} |A) = \frac{P(A \cap C_{j})}{P(A)} = \frac{P(C_{j} )}{P(A)} = \frac{p_{j} }{1-d_{i}p_{i} }$

as needed so part one is solved.

Solution to Part(2):

so we have now that if $j$ = $i$ , we get that:

$P(C_{j}|A ) = \frac{P(A \cap C_{j})}{P(A)}$

remember that:

$P(A|C_{j} ) = \frac{P(A \cap C_{j})}{P(C_{j})}$

this implies that:

$P(A \cap C_{j}) = P(C_{j}) \cdot P(A|C_{j}) = p_{i} (1-d_{i} )$

so we just need to combine the above relations to get:

$P(C_{j}|A) = \frac{p_{i} (1-d_{i} )}{1-d_{i}p_{i} }$

as needed so part two is solved.

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4 years ago

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Elan Coil [88]

The correct answer would be a because you have to multiply and get it

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3 years ago

2.85 rounded to the nearest hundredth A. 2.861 B. 2.849 C. 2.842 D. 2.805

blagie [28]

Answer:

B) 2.849

Step-by-step explanation:

Given: 2.85 which is rounded to the nearest hundredth place.

To find the number, the thousandth place must be greater than or equal to 5.

Here 2.849 has the thousandth place greater than 5

When we round off 2.849 to the nearest hundredth place, we get

2.85

Therefore, answer is B) 2.849

Hope this will helpful.

Thank you.

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4 years ago

Read 2 more answers

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suter [353]

Answer:
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Explanation:
The inequality is y ≤ –x + 1
There are two ways to do this. You can try the four options by seeing where they lie on the graph, or by inputting them into the inequality and seeing if they check out. I am going to do a bit of both.

I know that the solution cannot have two positive coordinates because the first quadrant is not part of the solution, so I won't guess A or C.
I'll try (3, –2) (which is option B).
On the graph, (3, –2) is on the line, which means it is part of the solution because the line is solid and the inequality is a greater than or equal to sign.
Try it in the inequality:
y ≤ –x + 1
–2 ≤ –3 + 1
–2 ≤ –2 yes this checks out.

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