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True [87]
3 years ago
7

How many x-intercepts would the function shown below have? f(x) = -5x (2x + 1)? (x² – 6)(x² + 9)

Mathematics
1 answer:
BabaBlast [244]3 years ago
5 0

Step-by-step explanation:

Here we have

f

(

x

)

=

2

x

2

(

x

2

−

9

)

, which can be factorized as

f

(

x

)

=

2

x

2

(

x

+

3

)

(

x

−

3

)

As there is no common factor between numerator and denominator, there s no hole.

Further vertical asymptotes are

x

=

−

3

and

x

=

3

and as

f

(

x

)

=

2

x

2

(

x

2

−

9

)

=

2

1

−

9

x

2

, as

x

→

∞

,

f

(

x

)

→

2

, hence horizontal asymptote is

y

=

2

.

Observe that

f

(

−

x

)

=

f

(

x

)

and hence graph is symmetric w.r.t.

y

-axis. Further as

x

=

0

,

f

(

x

)

=

0

. Using calculas we can find that at

(

0

,

0

)

there is a local maxima as

d

y

d

x

=

−

36

x

(

x

2

−

9

)

2

and at

x

=

0

it is

0

. Further while for

x

<

−

3

and

x

>

3

, function is positive, for

−

3

<

x

<

3

function is negative.

Now take a few values of

x

say

{

−

10

,

−

7

,

−

4

,

−

2

,

−

1

,

1

,

2

,

4

,

7

,

10

}

and corresponding values of

f

(

x

)

are

{

2

18

91

,

2

9

20

,

4

4

7

,

−

1

3

5

,

−

1

4

,

−

1

4

,

−

1

3

5

,

4

4

7

,

2

9

20

,

2

18

91

}

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