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madam [21]
3 years ago
6

If you apply the changes below to the absolute value parent function, f(x) = |x|, what is the equation of the new function?Shift

5 units to the left.Shift 4 units down.
Mathematics
2 answers:
Jlenok [28]3 years ago
6 0
Hi! Sorry if this is wrong, but I believe it would be f(x)= |x+5|-4. This is because it shifts to the left, so it is adding 5 to the x in the absolute value bars. And it shifting 4 units down would be negative. Hope this helps!
lesya692 [45]3 years ago
3 0

Answer:

f(x) = |x+5|; f(x) = |x|-4

Step-by-step explanation:

A horizontal shift (left or right) will be shown in the function within the operation applied to x.

Since the operation applied to x is absolute value, this means this shift will be shown within the absolute value bars.

A horizontal shift left means the value is added to x before the operator; this means we have x+5 within the bars, or

f(x) = |x+5|

A vertical shift (up or down) will be shown in the function outside of the operation applied to x.

For this function, this means the vertical shift will be outside of the bars; since it is a shift down, we subtract:

f(x) = |x|-4

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Teacl Smolts are young salmon at a stage when their skin becomes covered with silvery scales and they start to migrate from fres
erma4kov [3.2K]

Answer:

a) s = 8.81

b) Q1 = 43.4, Q2 = 49.4, Q3 = 57.35

c) See below

Step-by-step explanation:

(a) Find the standard deviation of the reflectance for these smolts. (Round your answer to two decimal places.)

In order to find the standard deviation, we need the mean first. The mean is defined as

\bar x=\displaystyle\frac{\displaystyle\sum_{i=1}^{n}x_i}{n}

where the x_i are the values of the data collected and n=50 the size of the sample.

So, the mean is

\bar x=50.882

Now, the standard deviation of the sample is defined as  

s=\sqrt{\displaystyle\frac{\displaystyle\sum_{i=1}^n(x_i-\bar x)^2}{n-1}}

and we have that our standard deviation is

s = 8.81

(b) Find the quartiles of the reflectance for these smolts

To find the quartiles, we must sort the data from lowest to largest:  

33.6,  37.7,  38.3,  38.7,  42,  42,  42.2,  42.4,  42.7,  42.8,  42.9,  43.1,  43.7,  43.8,  44.2,  44.6,  45.5,  45.7,  46.3,  46.6,  47.4,  47.6,  47.7,  47.9,  49.2,  49.6,  50.5,  50.9,  51.3,  53,  53.9,  54.8,  54.9,  55.5,  56,  56,  56.2,  57.1,  57.6,  58.3,  59,  59.5,  60.4,  63.2,  63.4,  63.5,  64.6,  68,  69.1,  69.2

The <em>first quartile</em> is the number between the 12th and the 13th data (so 25% of the data are below it and 75% above it)

So the 1st quartile is

Q_1=\displaystyle\frac{43.1+43.7}{2}=43.4

The <em>2nd quartile is the median</em>, the point between the 25th and 26th data, it splits the data in two halves.

Q_2=\displaystyle\frac{49.2+49.6}{2}=49.4

The 3rd quartile is the point between the 38th and 39th data (so 75% of the data are below it and 25% above it)

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(c) Do you prefer the standard deviation or the quartiles as a measure of spread for these data? Give reasons for your preference.

In this case, we prefer the quartiles as a measure of spread since the data are very scattered around the mean and there is no a central tendency.

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