The function f (x) = x^4 has an axis of symmetry the vertical axis y.
True or False?
True.
One way to check is of course to plot the given function. You'll see it has an axis of symmetry at y-axis.
Another way is to replace x with -x. If the resulting function is the same as the original, it has an axis of symmetry at the y-axis. Like, in the given function,
f(x) = x^4
f(-x) = (-x)^4
f(-x) = x^4 = f(x)
Hope this helps~ :)
YES!!!! thank you very much!!
False.
To determine if a function has an axis of symmetry, we need to check if it is symmetric with respect to the y-axis. The axis of symmetry of a function is a vertical line that divides the function into two symmetric parts.
In the case of the function f(x) = x^4, we can inspect the function to determine if it is symmetric with respect to the y-axis. We observe that the graph of f(x) = x^4 is centered at the origin (0,0). This means that it is symmetric with respect to the y-axis.
Therefore, the statement is true. The function f(x) = x^4 has an axis of symmetry along the vertical axis, the y-axis.