We have a property for odd functions, which is given below. Let f(x) be an odd function then it must satisfy the below - mentioned property.
Now, we have been given the function
For this function to be odd, it must satisfy the above written property.
Replace x with -x, we get
And, we have to also find
Hence, in order to the given function to be an odd function, we must determine whether 9-4(-x)^2 is equivalent to -(9-4x^2) or not.
Therefore, C is the correct option.
Answer:
The vertex of the parabola is the maximum value, i.e.,(-1,0). The function is increasing x<-1. the function is decreasing x>-1. the domain of the function is all real numbers. the range of the function is all real numbers less than or equal to 0.
Step-by-step explanation:
The given function is
....(1)
The general vertex form of the parabola is
.....(2)
Where, (h,k) is vertex and a is stretch factor.
On comparing (1) and (2), we get
The vertex of the parabola is (-1,0). Since a=-1<1 so it is a downward parabola.
The axis of symmetry is x=-1. So, before -1 the function is increasing and after -1 the function is decreasing.
The vertex of a downward parabola is the point of maxima. So, the rang of the function can not exceed 0.
Therefore the vertex of the parabola is the maximum value, i.e.,(-1,0). The function is increasing x<-1. the function is decreasing x>-1. the domain of the function is all real numbers. the range of the function is all real numbers less than or equal to 0.