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Answer:
The function that represents g(x) is the third choice: g(x) = (x − 4)^2 + 9
Step-by-step explanation:
The original function has been shifted 9 units up (a vertical transformation). To show a vertical transformation, all we have to do is either add or subtract at the end of the function.
<em>To show a shift upwards, we add the value of change. </em>
<em>To show a shift downwards, we subtract the value of change. </em>
In this case, the original function f(x) = was translated 9 units up. Since we shifted up, we simply add 9 to the end of the function: g(x) =
+ 9
The original function has also been shifted 4 units to the right. This is a horizontal transformation. To show a horizontal transformation, we need to either add or subtract within the function (within the parenthesis).
<em>To show a shift to the left, we add the value of change.</em>
<em>To show a shift to the right, we subtract the value of change.</em>
<u>*Notice: Moving left does NOT mean to subtract while moving right does NOT mean to add. The rules above are counterintuitive so pay attention when doing horizontal transformations. </u>
In this case, the original function f(x) = was translated 4 units to the right. Since we shifted right, we must subtract 4 units within the function/parenthesis: g(x) =
When we combine both vertical and horizontal changes, the only equation that follows these rules is the third choice: g(x) = (x − 4)^2 + 9
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