Which points lie on the graph of f(x) = log9x? -1/81, 2 0,1 1/9, -1 3, 243 9,1 81,2

Let

y=f(x)

we know that

applying property of logarithms

y= log9x is equal to

------> equation 1

so

case 1) (-1/81, 2)

x=-1/81

y=2

substitute the value of y in the equation 1 to obtain the value of x

81 is not equal to -1/81-------> the point does not belong to the graph

case 2) (0, 1)

x=0

y=1

substitute the value of y in the equation 1 to obtain the value of x

9 is not equal to 0-------> the point does not belong to the graph

case 3) (1/9, -1)

x=1/9

y=-1

substitute the value of y in the equation 1 to obtain the value of x

1/9 is equal to 1/9-------> the point belongs to the graph

case 4) (3, 243)

x=3

y=243

substitute the value of y in the equation 1 to obtain the value of x

9^{243} is not equal to 3-------> the point does not belong to the graph

case 5) (9, 1)

x=9

y=1

substitute the value of y in the equation 1 to obtain the value of x

9 is equal to 9-------> the point belongs to the graph

case 6) (81, 2)

x=81

y=2

substitute the value of y in the equation 1 to obtain the value of x

81 is equal to 81-------> the point belongs to the graph

The function is such that, performing the reverse operations of the function

on the output gives the input.

The points that lie on the graph are;

Reasons:

The given function is f(x) = log₉x

Therefore;

The ordered pair are in the form (x, f(x))

First option gives;

9² =  81 ≠ -1/81, therefore, (-1/81, 2) does not lie on the graph of f(x)

Second option;

9¹ = 9 ≠ 0, the second option is not on a point on the graph

Third option, x = , f(x) = -1 ;

9⁻¹ = , which corresponds with the form , therefore

Fourth option:

9¹ = 9 ≠ 1, does not lie on the graph

Fifth option, x = 81, y = 2;

9² = 81, therefore, the fifth option ordered pair can be obtained or expressed in the form , and therefore, lie on the graph of the function.

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the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !

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step-by-step explanation:

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