How do I use "logical reasoning" to determine the end behaivor or limit of a function

[GrannySmith]

How do I use "logical reasoning" to determine the end behaivor or limit of a function

Stuck on some problems in my homework. The direction says to use logical reasoning to determine the end behaivor of the function as x approaches infinity.

Example: f(x) = -(24)/x

I know what they mean for when x approaches infinity. I determine the end behavior of the right side of the graph. But without graphing this function on a graphing calculator, how would one determine the end behavior?

 

[HallsofIvy]

Stuck on some problems in my homework. The direction says to use logical reasoning to determine the end behaivor of the function as x approaches infinity.

Example: f(x) = -(24)/x

I know what they mean for when x approaches infinity. I determine the end behavior of the right side of the graph. But without graphing this function on a graphing calculator, how would one determine the end behavior?

Did you calculate a few values? f(10)= -24/10= -2.4. f(100)= -24/100= -0.24. f(1000)= -24/1000= -0.024. f(10000)+ -24/10000= -0.0024. etc.

What is happening to f(x) as x gets larger and larger (approaches infinity)?

 

[GrannySmith]

Did you calculate a few values? f(10)= -24/10= -2.4. f(100)= -24/100= -0.24. f(1000)= -24/1000= -0.024. f(10000)+ -24/10000= -0.0024. etc.

What is happening to f(x) as x gets larger and larger (approaches infinity)?

I see what you did there. y approaches infinity as x gets larger.

Now, do I do what you did there for more complex equations? For example, a square root function. One with cubes, and even greater powers.

Does one just simply have to go through the pain of calculating all of this in their head, or is a calculator needed?

 

[Mrspi]

I see what you did there. y approaches infinity as x gets larger.

Now, do I do what you did there for more complex equations? For example, a square root function. One with cubes, and even greater powers.

Does one just simply have to go through the pain of calculating all of this in their head, or is a calculator needed?

y = f(x) = -24/x

From the examples given in the previous post, you should see that as x gets larger, -24/x gets closer and closer to 0. If x = 100,000, y = -24/100000 or -0.00024, which is close to 0.

As x increases in value, y should approach 0 from the left side (since -24 divided by any POSITIVE number will produce a negative result). So, as x gets larger, y isn't going to approach infinity.....it is going to approach 0.

Using your "number sense" may help you see the "end behavior" of functions; a calculator isn't necessary, but it is helpful to look at the graph of a function to determine its end behavior.