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# End Behavior

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"What is the End Behavior and Average Rate of Change for each function?"

1. f(x) = x²

2. f(x) = |x|

3. f(x) = √x

4. f(x) = log x

5. f(x) = 2^x

6. f(x) = 1/x

I graphed each one into Desmos but I don't know how to find the end behavior or the rate of change. Please help. I'm very confused. Thanks.

Jan 31, 2019

#1
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"What is the End Behavior and Average Rate of Change for each function?"

I wouldn't expect you to know the average rate of change unless you have had Calculus

Thus....unless.....you will just have to take my word for this part of the answer

1. f(x) = x²

End behavior = up at both ends.....average rate of change =  2x

2. f(x) = |x|

End behavior = up at both ends   ......average rate of change =    x / √x^2

3. f(x) = √x

End behavior....on the left end, x =0 and y = 0     at the right end, "up"  .....avg rate of change =  1 / [2√x ]

4. f(x) = log x

End behavior .....tends toward neg  infinitiy as x approaches 0 from the right.....up on the right

Avg rate of change = 1 / x

5. f(x) = 2^x

End behavior.......tends toward y = 0 on the left side .....positive infinity on the right

Avg rate of changle =   Ln (2)*2^x

6. f(x) = 1/x

End behavior........tends toward y = 0 on the left  and  tends toward neg inf as x approaches 0 from the left

Not defined at x = 0

Tends toward positive infinity as x approaches 0 from the right.....and then toward y = 0 on the right

Avg rate of change =  log x   Jan 31, 2019
#2
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Thank you so much! I haven't had Calculus yet. My school does not teach a calculus class thankfully. I appreciate your help!

Guest Jan 31, 2019