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1103124301

Level:

The picture shows graphs of two quadratic functions

f_{1} (x)

and

f_{2} (x)

. Find the unknown real positive constant

a

(as shown in the picture) such that the value of the definite integral

\int_{- 1}^{1} f_{1} (x) d x

is greater by

8

than the value of the definite integral

\int_{- 1}^{1} f_{2} (x) d x

a = 3

a = 1

a = 4

a = 6

1003259610

Level:

Let there be a function

f (x) = \frac{a x^{2}}{x - b}

a

b \in R

. Determine the values of

a

b

, such that the line

y = 3 x + 2

is an asymptote of the graph of the function

f

a = 3

b = \frac{2}{3}

a = 3

b = \frac{4}{3}

a = 3

b = 2

a = 2

b = \frac{3}{2}

there are no such

a

b

1003259609

Level:

Determine the values of

a

b

(

a

b \in R

) such that the line

y = 0

is an asymptote of the graph of the function

f (x) = \frac{x}{a x - 1} + b x

there are no such

a

b

a \in R ∖ {1}

b = 0

a = 0

b = 0

a \in R

b = 0

1003259608

Level:

Determine the values of

a

b

(

a

b \in R

) such that the line

y = 2 x + \frac{1}{3}

is an asymptote of the graph of the function

f (x) = \frac{x}{a x - 1} + b x

a = 3

b = 2

a = \frac{1}{2}

b = 3

a = 2

b = \frac{1}{3}

a = \frac{1}{2}

b = \frac{1}{3}

a = \frac{1}{3}

b = 2

1003259607

Level:

Find all the asymptotes of the graph of the function

f (x) = x e^{\frac{1}{x}}

x = 0

y = x + 1

x = 0

y = x - 1

x = 0

there is no an asymptote

x = 0

y = 1

1003259606

Level:

Find all the asymptotes of the graph of the function

f (x) = e^{\frac{1}{x}}

x = 0

y = 1

x = 0

y = 0

x = 0

there is no an asymptote

x = 0

y = - 1

1003259605

Level:

Find all the asymptotes of the graph of the function

f (x) = \frac{1}{x - 2} + x - 1

x = 2

y = x - 1

x = 2

y = x

x = 2

x = 2

y = 1

x = 2

y = - 1

1003259604

Level:

Find all the asymptotes of the graph of the function

f (x) = \frac{1}{1 - x^{2}}

x = 1

x = - 1

y = 0

x = 1

x = - 1

x = 1

x = - 1

y = 1

y = 1

y = - 1

y = 0

x = 1

y = 0

1003259603

Level:

Find all the asymptotes of the graph of the function

f (x) = \frac{x}{x^{2} + 1}

y = 0

there is no an asymptote

x = 0

x = - 1

y = 0

1003259602

Level:

Find all the asymptotes of the graph of the function

f (x) = x + \frac{2 x}{x^{2} - 1}

x = - 1

x = 1

y = x

x = - 1

x = 1

y = 1

x = - 1

x = 1

y = x + 1

x = - 1

x = 1

x = - 1

x = 1

y = 0

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1103124301

1003259610

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1003259608

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1003259605

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1003259602

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