Which statements about the graph of a function, its additive inverse, and its multiplicative inverse are true? Check all that apply.The sum of the function and its additive inverse is 0.The function and its additive inverse have symmetry over the x-axis.The function and its additive inverse have symmetry over the y-axis.The product of the function and its multiplicative inverse is 1.The function and its multiplicative inverse have rotational symmetry.
Answer
A
The sum of the function and its additive inverse is 0.
B
The function and its additive inverse have symmetry over the x-axis.
C
The function and its additive inverse have symmetry over the y-axis.
D
The product of the function and its multiplicative inverse is 1.
E
The function and its multiplicative inverse have rotational symmetry.
Explanation
If the function is y = f(x), its additive inverse is y = −f(x). Their values add to f(x) + (−f(x)) = 0, and their graphs are reflections of each other across the x-axis. Their product with the multiplicative inverse is f(x) · 1/f(x) = 1 wherever f(x) ≠ 0. These graphs do not generally have symmetry over the y-axis or rotational symmetry.
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