Answer: 7
Step-by-step explanation:
Which series of transformations takes the graph of f(x)=3x−8 to the graph of g(x)=−3x+12 ?
2 answers:
D.) reflect the graph about the x-axis and translate 4 units up
Explanation:
Before to identify the correct choice, let's see the definition of reflection along the x-axis and the y-axis:
1- A reflection of about the x-axis can be done by changing
into
. This means that if we have a line in the form
a reflection about the x-axis can be done by changing the function into
2- A reflection of about the y-axis can be done by changing
into
. This means that if we have a line in the form
a reflection about the x-axis can be done by replacing all the x with -x:
Back to our exercise:
The original function is . The final function is
. First of all, we immediately notice that both the signs of m and q have been changed: therefore, it must be a reflection about the x-axis, so we can discard option B.
The reflection of f(x) about the x-axis is
We see that the y-intercept is +8, while in g(x) the y-intercept is +12. In order to match the two functions, we must translate f'(x) up by 4 units, so that we get
which corresponds to g(x). So, the correct option is D.
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Answer:
Unfortunately, your answer is not right.
Step-by-step explanation:
The functions whose graphs do not have asymptotes are the power and the root.
The power function has no asymptote, its domain and rank are all the real.
To verify that the power function does not have an asymptote, let us make the following analysis:
The function , when x approaches infinity, where does y tend? Of course it tends to infinity as well, therefore it has no horizontal asymptotes (and neither vertical nor oblique)
With respect to the function we can verify that if it has asymptote horizontal in y = 0. Since when x approaches infinity the function is closer to the value 0.
For example: 1/2 = 0.5; 1/1000 = 0.001; 1/100000 = 0.00001 and so on. As "x" grows "y" approaches zero
Also, when x approaches 0, the function approaches infinity, in other words, when x tends to 0 y tends to infinity. For example: 1 / 0.5 = 2; 1 / 0.1 = 10; 1 / 0.01 = 100 and so on. This means that the function also has an asymptote at x = 0
Answer:
a)
b) The should sample at least 293 small claims.
Step-by-step explanation:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
So it is z with a pvalue of , so
, which means that the answer of question a is z = 1.645.
Now, find the margin of error M as such
In which is the standard deviation of the population and n is the size of the sample.
(b) If the group wants their estimate to have a maximum error of $12, how many small claims should they sample?
They should sample at least n small claims, in which n is found when
. So
The should sample at least 293 small claims.