Question

determine whether the intervals over which the function is increasing, decreasing, or constant and determine whether the function is odd, even or neither. f(x)= {2x+1, x^2-2 (piece wise function)

Answer 1

for what values of x is it 2x+1 and for what values is it x^2-2?

Answer 2

um for 2x+1 x is less than or equal to -1 and for x^2-2 is x > -1

Answer 3

okay, so you need to take the second derivative in order to find turning points, so for 2x-1 the second derivative is zero so no turning points. the first derivative is 2 so it is always increasing. for x^2-2 the first derivative is 2x and the second is 2, so it will have a turning point at x=0, will decrease for x < 0 and increase for x > 0.

2x-1 is odd because f(x) is not equal to f(-x)
x^2-2 is even because f(x) is equal to f(-x) (when you square a negative number, it becomes positive)

i hope this helps

Answer 4

2x+1*