SOLUTION: Which of the following is a transformation applied to the base function f(x)=-1\5(10^x+7)+12? A horizontal translation 12 to the right A reflection in the y -axis A horizont

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Question 1139317: Which of the following is a transformation applied to the base function f(x)=-1\5(10^x+7)+12?
A horizontal translation 12 to the right
A reflection in the y -axis
A horizontal stretch by a factor of 5
A vertical compression by a factor of 1/5
Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


(1) The function you show is not the base function; it is a transformed function.

(2) The function as you show it is this: -1%5C5%2810%5Ex%2B7%29%2B12

The backslash ("\") is not used to represent division (fractions); the program on this web site that interprets expressions simply ignores the backslash, creating the coefficient "-15". Using the correct symbol for representing fractions, your transformed function is -1%2F5%2810%5Ex%2B7%29%2B12

That clearly is not what you want; the entire coefficient "-1/5" must be in parentheses: %28-1%2F5%29%2810%5Ex%2B7%29%2B12

Finally, it is highly probable that, in the transformed function, the "+7" is supposed to be part of the exponent; so you need to put the entire exponent in parentheses: %28-1%2F5%29%2810%5E%28x%2B7%29%29%2B12

So the base function is apparently 10%5Ex

Let's look now at the transformations that are made to this base function, in the order that they are made (as determined by standard order of operations).

10%5E%28x%2B7%29 (replace x with x+7) represents a horizontal shift of 7 to the left.
%28-1%2F5%2910%5E%28x%2B7%29 (add the coefficient (-1/5)) represents a reflection in the x-axis and a vertical compression by a factor of 1/5.
%28-1%2F5%29%2810%5Ex%2B7%29%2B12 (adding the "+12" at the end) represents a vertical shift of +12.
There is no horizontal stretch or compression; that would be indicated by something like 10%5E%283x%29.

Only one of those transformations is one of the answer choices.