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laiz [17]
3 years ago
15

Show why, for linear functions, a vertical translation is equivalent to a horizontal translation. For a linear function, what ho

rizontal translation is equivalent to a vertical translation of 3 units up?
Mathematics
1 answer:
V125BC [204]3 years ago
8 0

Explanation:

A) For the function ...

f(x) = mx + b

the vertical translation by k makes the function ...

g(x) = f(x) + k = mx + b + k

This can be rewritten as ...

g(x) = m(x +k/m) +b = f(x+k/m)

That is, the vertical translation by k is equivalent to a horizontal translation by -k/m, where m is the slope of the linear function.

___

B) For a vertical translation of 3, the equivalent horizontal translation is ...

-k/m for k=3

= -3/m . . . . . where m is the slope of the function

_____

Please note that there is no equivalent for m=0.

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The maximum height of the diver would be the y value of the vertex of the graph. The vertex of the graph is (1,4). The maximum height of the diver is 4 meters.
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Can someone help me with this
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The answer is:

x=-8

Because:

If you pick a number(-8) to fill in the equation written below

5x+20+5x=5x-20

After applying the -8 to x you get

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5 0
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The table below represents the function F. 3 7 F(x) 4 15 5 31 7 127 8 255 The equation that represents this function is?​
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The table is an exponential function, and the equation that represents this function is f(x) =2^x -1

<h3>The equation of the table</h3>

The table is given as:

x   F(x)

4    15

5    31

7    127

8    255

Rewrite the table as:

x   F(x)

4    16 - 1

5    32 - 1

7    128 - 1

8    256 - 1

Express as a base of 2

x   F(x)

4    2⁴ - 1

5    2⁵- 1

7    2⁷ - 1

8    2⁸ - 1

Notice that the function is 1 subtracted from 2 raised to the power of the input.

This is represented as:

f(x) =2^x -1

Hence, the equation of the table is f(x) =2^x -1

Read more about exponential functions at

brainly.com/question/9608962

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