Question

Which of the following represents a transformed version of the function h(x)=−(x+4)² −3, incorporating at least two types of transformations out of the four possible types?

A) h(x)=(x+4)²-3
B) h(x)=−(x−4)²-3
C) h(x)=−(x+4)²+3
D) h(x)=−(x+4)²+5

Answer 1

The transformed function h(x) = -(x-4)² - 3 represents a reflection across the y-axis and a horizontal translation to the right, incorporating at least two types of transformations from the original function h(x) = -(x+4)² - 3.

Step-by-step explanation:

The question involves identifying a function that has gone through at least two types of transformations from its original form h(x) = -(x+4)² - 3. The types of transformations we look for include translation (shifting up/down or left/right), reflection (flipping over the x or y-axis), stretching or compressing vertically or horizontally, and rotations (although rotations are not commonly considered in basic function transformations).

Comparing the options provided with the original function, we can analyze the changes:

• A) h(x) = (x+4)² - 3: This represents a reflection across the y-axis.
• B) h(x) = -(x-4)² - 3: This represents a horizontal translation to the right by 8 units.
• C) h(x) = -(x+4)² + 3: This is a vertical translation upward by 6 units.
• D) h(x) = -(x+4)² + 5: This is a vertical translation upward by 8 units.

Option B fits the description best, as it has undergone a reflection (because the negative sign in front of the quadratic term is maintained, indicating that the reflection over the x-axis is preserved) and also a horizontal translation (the +4 in the original function has become -4, indicating a shift to the right by 8 units).