to have an even function f(x) must equal f(-x), i.e.
there has to be a reflection in the y-axis
to have an odd function f(x) must be -f(-x), or
a reflection in the origin.
clearly the first one is a parabola whose axis in NOT the y-axis and f(x) is not -f(x) , so it is neither even nor odd
(Just try any two opposite numbers)
your second equation is odd
the domain is the choice of x's you can make,
clearly for both you may use any x, so the domain is the set of real numbers
the range is the resulting values you get for y after using those x's
for the parabola, it would be any value greater than the y of your vertex.
for the second, since you can take cube roots of both positive and negative numbers, the range would be the set of real numbers.
Where do the graphs cross the x and y axis?
Since the vertex of the parabola is above the x-axis, there cannot be any x-intercepts, but the y-intercept is 6 (when x=0)
the origin (0,0) is the x and y intercept of your second equation.
Can anyone tell me if these functions are odd, even, or neither. Also, what is the domain, range, x-intercept, and y-intercept of these functions?
1. f(x) = x^2 - 3x + 6
2. f(x) = cubicroot(x)
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