Math
posted by Jayson .
Verify these answers :]
Would be thankies~
1. Determine the intervals in which the reciprocal function of f(x)= x^2+1 is increasing.
a) (0,∞)
b) (∞, 0)
c) (∞,∞)
d) (1,∞)
Answer: D

2. Determine the point(s) where f(x)=2x^21 and its reciprocal function intersect.
a) (1,1)
b) (1,1)
c) (1,1) and (1,1)
d) (1,1), (1,1) and (0,1)
Answer:D

3. Identify the vertical and horizontal asympototes of f(x)=x4/2x+1
a)vertical x=4, horizontal:y=1/2
b)vertical x=4, horizontal:y=1/2
c)vertical x=1/2, horizontal:y=1/2
d)vertical x=1/2, horizontal:y=1/2
Answer: A

4. State the equation of the rational function that meets these conditions:
vertical asympotote at x=2
Horizontal asympotote at y=1
increases on each interval of its domain
xintecept is (3,0)
a) y=x+3/x+2
b) y=x3/x+2
c) y=x+3/x2
d) y=x3/x2
Answer: A

5. state the equation of f(x) is D= [XERx≠2/3] and the yintercept is (0,1/2).
a) f(x)=2x+1/3x2
b) f(x)=x1/3x2
c) f(x)=x+1/3x+2
d) f(x)=2x+1/3x+2
Answer is B?

1.
y = x^2+1
This is always positive, with its minimum value at x=0, where y=1. The range is [1,∞0, but that's not where it is increasing.
Now, the question asks about the reciprocal function z = 1/y
z = 1/(x^2+1)
Where y increases, z decreases, and vice versa. So, z is increasing on (∞, 0), answer B
2. OK
3. None of the above. Would be C, but the horizontal is y = 1/2. I assume you wanted (x4)/(2x+1)
4. vertical at x=2 means C or D
horizontal at y=1 keeps C or D
intercept at (3,0) means D
increasing keeps D
so, D.
5. D = x not 2/3 means A or B
yintercept at (0,1/2) means B.
So, B.