Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply.
2 answers:
Answer: g(x) > h(x) when x = -1.
For x greater than zero, g(x) is greater than h(x).
For x less than zero, g(x) is greater than h(x).
Step-by-step explanation:
Given the functions: and
At x = 0, and
. Therefore, g(0) equals h(0).
Hence, statements claiming that for all x, g(x) is always greater than h(x), or vice versa, are incorrect.
At x = -1, and
So, g(x) > h(x) for x = -1............................(1)
At x = 3, and
Therefore, g(x) > h(x) at x = 3........................(2)
Which disproves the statement that g(x) < h(x) for x = 3.
From points (1) and (2):
For any positive x, g(x) > h(x).
For any negative x, g(x) > h(x).
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Using a direct approach:
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For more information:
1. What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0)