SOLUTION: Given f(x)=-x3+x2+3x+4, find f(-1), f(0), and f(1) The 3 and the 2 are powers of the x.

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Question 117410: Given f(x)=-x3+x2+3x+4, find f(-1), f(0), and f(1)
The 3 and the 2 are powers of the x.
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

Let's evaluate f%28-1%29


f%28x%29=-1x%5E3%2B1x%5E2-3x%2B4 Start with the given function.


f%28-1%29=-1%28-1%29%5E3%2B1%28-1%29%5E2-3%28-1%29%2B4 Plug in x=-1. In other words, replace each x with -1.


f%28-1%29=-1%28-1%29%2B1%28-1%29%5E2-3%28-1%29%2B4 Evaluate %28-1%29%5E3 to get -1.


f%28-1%29=-1%28-1%29%2B1%281%29-3%28-1%29%2B4 Evaluate %28-1%29%5E2 to get 1.


f%28-1%29=%2B1%2B1%281%29-3%28-1%29%2B4 Multiply -1 and -1 to get 1


f%28-1%29=%2B1%2B1-3%28-1%29%2B4 Multiply 1 and 1 to get 1


f%28-1%29=%2B1%2B1%2B3%2B4 Multiply -3 and -1 to get 3


f%28-1%29=9 Now combine like terms


-----------Now let's evaluate another value---------


Let's evaluate f%280%29


f%28x%29=-1x%5E3%2B1x%5E2-3x%2B4 Start with the given function.


f%280%29=-1%280%29%5E3%2B1%280%29%5E2-3%280%29%2B4 Plug in x=0. In other words, replace each x with 0.


f%280%29=-1%280%29%2B1%280%29%5E2-3%280%29%2B4 Evaluate %280%29%5E3 to get 0.


f%280%29=-1%280%29%2B1%280%29-3%280%29%2B4 Evaluate %280%29%5E2 to get 0.


f%280%29=%2B0%2B1%280%29-3%280%29%2B4 Multiply -1 and 0 to get 0


f%280%29=%2B0%2B0-3%280%29%2B4 Multiply 1 and 0 to get 0


f%280%29=%2B0%2B0%2B0%2B4 Multiply -3 and 0 to get 0


f%280%29=4 Now combine like terms


-----------Now let's evaluate another value---------


Let's evaluate f%281%29


f%28x%29=-1x%5E3%2B1x%5E2-3x%2B4 Start with the given function.


f%281%29=-1%281%29%5E3%2B1%281%29%5E2-3%281%29%2B4 Plug in x=1. In other words, replace each x with 1.


f%281%29=-1%281%29%2B1%281%29%5E2-3%281%29%2B4 Evaluate %281%29%5E3 to get 1.


f%281%29=-1%281%29%2B1%281%29-3%281%29%2B4 Evaluate %281%29%5E2 to get 1.


f%281%29=-1%2B1%281%29-3%281%29%2B4 Multiply -1 and 1 to get -1


f%281%29=-1%2B1-3%281%29%2B4 Multiply 1 and 1 to get 1


f%281%29=-1%2B1-3%2B4 Multiply -3 and 1 to get -3


f%281%29=1 Now combine like terms