An even function is decreasing and concave down in the first quadrant. How does the function behave in the second quadrant?
A) It is decreasing and concave down
B) It is increasing and concave up
C) It is increasing and concave down
D) It is decreasing and concave up

Question

Quizplus · Accepted Answer

Even functions are symmetric about the y-axis, meaning their behavior in the second quadrant mirrors their behavior in the first quadrant but with the direction of increase/decrease reversed. Since the function is decreasing in the first quadrant, it will be increasing in the second quadrant. However, concavity is preserved across the y-axis, so if it's concave down in the first quadrant, it remains concave down in the second quadrant.

An Even Function Is Decreasing and Concave Down in the First