Show why, for linear functions, a vertical translation is equivalent to a horizontal translation. for a linear function, what horizontal translation is equivalent to a vertical translation of 3 units up?

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.

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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.

14.3

step-by-step explanation:

add all the numbers together.

9 + 12 + 15 + 16 + 17 + 17 = 86

now, divide 86 by how many numbers we have: 6.

86 / 6 = 14.3