Question

The graphs of f(x) and g(x) are shown below:

If f(x) = (x + 7)^2, which of the following is g(x), based on the translation?

see attached :)

Answer 1

B.) g(x) = (x + 5)²

Explanation:

When you add numbers to the "x" value within parentheses, you shift the function to the left. When you subtract numbers from the "x" value, you shift the function to the right. Since the origin (lowest point) of the graph lies within the negative region (second quadrant), there must be a value added to "x".

To know how large of a number is added, you can always use the guess-and-check method. You can do this by plugging in 0 for "y" to identify which equation gives the accurate data point. The correct value that should be added is (5) because on the graph, when "y" is 0, the "x" value is (5).

Therefore, since there are no other transformations to the parent function, the correct equation is g(x) = (x+ 5)².