Answer:
1) B. (-infinity,-2) U (0.6,infinity)
2) a(2x-1)(x+4)(x+1) where a is a constant multiple.
3) C. [tex]\text{ As } x \right \infty,f \rightarrow \infty \text{ and }x \right -\infty,f \rightarrow -\infty[/tex]
Step-by-step explanation:
1)
The function is rising before x=-2.
The function is decreasing while x is between -2 and 0.6.
The function is rising after x=0.6
A.
On the interval (0,-9.5), the function decreases then increases so the function isn't purely increasing on this interval.
B.
On the in interval (-infinity,-2) U (0.6, infinity), the function is rising on the first interval and also rising on the second interval as stated above.
C.
On the interval (-2,0.6), the function is decreasing since it is falling.
D.
On the interval (-infinity,0) the function is rising then falling.
On the interval (-9.5,infinity) the function is rising, falling, then rising again.
So of these choices, the answer is B.
2)
If c is a zero, then x-c is a factor.
If x=1/2 is a zero, then x-1/2 is a factor.
Or!
x=1/2
Multiply both sides by 2:
2x=1
Subtract 1 on both sides:
2x-1=0
So instead of saying x-1/2 is a factor, you could use 2x-1 instead. We are going to slap a constant multiple of unknown value on the end product anyways.
If x=-4 is a zero, then x+4 is a factor.
If x=-1 is a zero, then x+1 is a factor.
So putting this all together, a polynomial with these zeros could be:
a(2x-1)(x+4)(x+1)
where a is an unknown constant multiple.
3) The graph is pointing down on the left side because that is where the curve continues at.
So on the left side, that means as x approaches negative infinity, f approaches negative infinity because of the down part.
[tex]x \right -\infty[/tex] implies [tex]f \rightarrow -\infty[/tex]
The graph is point up on the right side because that is where the curve continues at.
So on the right side, that means as x approaches positive infinity, f approaches positive infinity because of the up part.
[tex]x \right \infty[/tex] implies [tex]f \rightarrow \infty[/tex]
This in one line says:
[tex]\text{ As } x \right \infty,f \rightarrow \infty \text{ and }x \right -\infty,f \rightarrow -\infty[/tex]
