Math

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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
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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?

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  1. 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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