Answer:
a) x³, 1/x, x, sin(x)
Step-by-step explanation:
You want to know which list of functions has the same graph when reflected across both the y- and x-axes.
Odd function
Reflection across the y-axis transforms the function to ...
f(x) ⇒ f(-x)
Reflection across the x-axis transforms the function to ...
f(x) ⇒ -f(x)
Hence, reflection across both axes transforms the function to ...
f(x) ⇒ -f(-x)
A function that has the characteristic that f(x) = -f(-x) is an odd function. Its graph is symmetrical about the origin. We can check to see if the functions of interest match this definition of an odd function:
x³ = -(-x)³ . . . . true
1/x = -(1/-x) . . . . true
x = -(-x) . . . . true
sin(x) = -sin(-x) . . . . true
cos(x) = -cos(-x) . . . . false
e^x = -e^-x . . . . false
|x| = -|-x| . . . . false
The basic functions that are odd are ...
x³, 1/x, x, sin(x)
