Reflections and translations are instances of transformation.
<em>The rule of function g for the given reflection and translation is </em><em />
<em />
Given
<u>The rule of translating 5 units up is:</u>
So, we have:
<u>The rule of reflecting about the y-axis is:</u>
So, we have:
Hence, the rule of function g is:
Read more about function transformations at:
Answer:
see below
Step-by-step explanation:
The tangent function has been shifted upward by 2 units, but there has been no horizontal scaling. Any horizontal offset must be equal to some number of whole periods.
Choices A and B show tan( )+2, the correct vertical offset. However, choice A has a horizontal scale factor of 2. The correct choice is B, which has no horizontal scaling (the coefficient of x is 1) and a horizontal offset of π, one full period.
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<em>Comment on horizontal scaling</em>
Horizontal scaling is different from vertical scaling in that using k·x in place of x <em>compresses</em> the graph horizontally by a factor of k. On the other hand, using k·f(x) in place of f(x) <em>expands</em> the graph vertically by a factor of k.
