The function g(x) = (x+5)2 - 7 is a transformation of parent function f (x) = x2. Which is the description of the transformation?
The function g(x) = (x+5)² - 7 is a transformation of the parent function f(x) = x². Let's break down how it's transformed:
1. Horizontal Translation: The "(x+5)" part of g(x) inside the parentheses indicates a horizontal shift of the graph of f(x) to the left by 5 units. This is because x is replaced by (x+5), meaning that for the function g(x) to have the same value as f(x), x has to be 5 units less. In the function notation, adding a positive number inside the parentheses with x shifts the graph to the left.
2. Vertical Translation: The "-7" at the end of the function g(x) indicates a downward shift of the graph of f(x) by 7 units. The entire graph is moved down on the y-axis by 7 units.
There are no reflections, stretches, or compressions in this transformation, as there are no negative signs in front of the (x+5)² term, nor are there any coefficients other than 1 multiplying the squared term.
So in summary, the transformation from f(x) = x² to g(x) = (x+5)² - 7 consists of:
- A horizontal shift left by 5 units.
- A vertical shift down by 7 units.