Question

The parent function f(x)=x ² is transformed to the new function g(x)=-(x+7) ²-5 Identify all the transformations that occurred to transform f(x) to g(x).

Answer 1

The parent function f(x) = x² is transformed to g(x) = -(x+7)² - 5 by a horizontal shift left by 7 units, a reflection across the x-axis, and a vertical shift downward by 5 units.

Step-by-step explanation:

The student is asking for the identification of transformations that occurred when the parent function f(x) = x² was changed to g(x) = -(x+7)² - 5. The transformations in question can be broken down as follows:

• Horizontal shift: The term (x+7) inside the square indicates a horizontal shift to the left by 7 units since the function f(x-d) represents a function translated in the positive x-direction by a distance d.
• Reflection: The negative sign in front of the square indicates a reflection across the x-axis, because it takes the parent function and multiplies it by -1, turning all positive values to negative and vice versa.
• Vertical shift: The -5 at the end of the function represents a vertical shift downwards by 5 units.