Question

Explain the transformations that were made to the following functions.

From: f(x) = 5 | x + 9 | - 8
To: f(x) = 5 | x + 7 | - 2

Answer 1

The function was transformed with a horizontal shift of 2 units to the right and a vertical shift of 6 units upwards.

Step-by-step explanation:

The transformation from f(x) = 5 | x + 9 | - 8 to f(x) = 5 | x + 7 | - 2 can be broken down into two parts. First, the transformation of the inner function from (x + 9) to (x + 7) represents a horizontal shift. Because we have an addition inside the absolute value, the function is shifted 2 units to the right, which is the difference between +9 and +7. Second, the transformation of the constant term from -8 to -2 represents a vertical shift. The function moves up by 6 units, as the difference between -8 and -2 is 6.