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kumpel [21]
3 years ago
13

The graph of f (x) = x + 5 is a vertical translation 5 units

Mathematics
1 answer:
irakobra [83]3 years ago
7 0

Answer:

A horizontal translation of 5 units to the left.

Step-by-step explanation:

Given the parent linear function:

\displaystyle f(x)=x

To shift vertically n units, we can simply add n to our function. Hence:

f(x)=x+n

So, a vertical shift of 5 units up implies that n=5. So:

f(x)=x+5

As given.

However, to shift a linear function horizontally, we substitute our x for (x-n), where n is the horizontal shift. So:

f(x-n)=(x-n)

Where n is the horizontal shift.

For example, if we shift our parent linear function 1 unit to the right, this means that n=1. Therefore, our new function will be:

f(x-1)=(x-1)

Or:

f(x)=x-1

We notice that this is also a vertical shift of 1 unit downwards.

Therefore, we want a number n such that -n=5.

So, n=-5.

Therefore, it we shift our function 5 units to the left, then n=-5.

Then, our function will be:

f(x-(-5))=(x+5)\text{ or } f(x)=x+5

Hence, we can achieve f(x)=x+5 from f(x)=x using a horizontal translation by translating our function 5 units to the left.

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Calculate the mean,median,and mode of the following set of data. Round to the nearest tenth 10,1,10,15,1,7,10,1,6,13
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Now for the median.

To find the median put all the numbers in order, then find the middle number.

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And finally, the mode.

To find the mode, find the number that appears the most. 

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In this case, there are two modes. 1, and 10.

Hopefully this helps! If you have any more questions or don't understand, feel free to DM me, and I'll get back to you ASAP! :)
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