Posted by **Jayson** on Wednesday, December 21, 2011 at 5:04pm.

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

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2. Determine the point(s) where f(x)=2x^2-1 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

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3. Identify the vertical and horizontal asympototes of f(x)=x-4/2x+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

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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

-x-intecept is (3,0)

a) y=x+3/x+2

b) y=x-3/x+2

c) y=x+3/x-2

d) y=x-3/x-2

Answer: A

-------------------------------------

5. state the equation of f(x) is D= [XER|x≠2/3] and the y-intercept is (0,1/2).

a) f(x)=2x+1/3x-2

b) f(x)=x-1/3x-2

c) f(x)=x+1/3x+2

d) f(x)=2x+1/3x+2

Answer is B?

- Math -
**Steve**, Wednesday, December 21, 2011 at 5:52pm
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 (x-4)/(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

y-intercept at (0,1/2) means B.

So, B.

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