00:01
Hi, from the question given that consider the given function polynomial function f of x is equal to x minus 1d whole cube times x plus 3d whole square.
00:13
So, in part a we need to find the y intercept and part b we need to find the x intercept and its multiplicity does it touch or cross the x axis.
00:23
So, for y intercept y intercept we need to set x is equal to 0.
00:29
So, if x is equal to 0 y is equal to f of x then y is equal to minus 1 cube 3 square which is equal to 9.
00:45
Therefore, y intercept is 9.
00:49
Now, let us move on to part b part b we need to find the x intercept and its multiplicity does it touch or cross the x axis.
00:56
So, x intercept is obtained by setting y is equal to 0.
01:03
So, for that 0 is equal to x minus 1d whole cube and x plus 3d whole square.
01:10
So, here the x intercept occurs at x is equal to 1 and x is equal to negative 3, but from this information x as the cube x as the cubic power x minus 1 as a cubic power.
01:28
Therefore, x minus 1 has odd multiplicity odd multiplicity 3.
01:41
Therefore, it crosses x axis and x plus 3 has even multiplicity 2.
02:05
So, it touches the x axis.
02:13
So, this is a diagrammatic representation for the given polynomial function.
02:17
So, here at x is equal to negative 3 it touches the x axis and at x is equal to positive 1 it crosses the x axis.
02:29
Now, for part c we need to find the end behavior.
02:32
So, from this graph as x tends to positive infinity.
02:36
So, this implies f of x also tends to positive infinity.
02:42
Similarly, if x tends to negative infinity then this implies f of x is also tends to negative infinity.
02:52
Now, let us move on to part d.
02:55
So, part d we need to graph the function with 3 of the x and y intercept and also 3 more points on the additional point on the graph...