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

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) (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:

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

That clearly is not what you want; the entire coefficient "-1/5" must be in parentheses:

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:

So the base function is apparently

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).

(replace x with x+7) represents a horizontal shift of 7 to the left.
(add the coefficient (-1/5)) represents a reflection in the x-axis and a vertical compression by a factor of 1/5.
(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 .

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