Question

Evaluate the piecewise defined function at the indicated values.
f(x) = {x2 + 4x if x ≤ −1
{x if −1 < x ≤ 1
{−1 if x > 1


f(-4)=..?

Answer 1

well,first we should say -4 is less\equal than -1 or not.

Answer 2

and it is!
\[-4 \le -1\]

Answer 3

ok and then..? haha

Answer 4

i will substitute the -4 to those three equations..? or i will do something else to before substitutuing..?

Answer 5

it's written for x less/equal than -1 we should use this:
x^2 + 4x

Answer 6

so (-4)^2 + 4(-4) = ?

Answer 7

16-16...?

Answer 8

yes! 0

Answer 9

so do you now what you should do?

Answer 10

now find f(5) please ;)

Answer 11

5 > 1 so what we should do?

Answer 12

f(5) to x^2 + 4x..?

Answer 13

no! for x < (or equal) -1 we should find x^2 + 4x and 5 is not < -1 , it's >1 .
and for x>1 we have -1,so for each x > 1 we have -1!
for example:
f(2) = -1
f(3) = -1
.
.
.
f(1000) = -1
got it?

Answer 14

sorry.. didnt get.. it... if x ≤ −1 this should mean x must be less that or equal to -1..? when -4 is subtituted to x^2 + 4x..? i didnt really get this question..im confuse at this questions.. sorry

Answer 15

well,let's start from the begining.
all the functions you have seen are like this:
f(x) = x^2
f(x) = x^2 - 2
or etc.
here we have another kind of functions that for each x that are less or equal than -1 , we should find x^2 + 4x!
so if x≤-1 , then f(x) = x^2 + 4x
but if x is bigger than -1 and is less/equal than 1 we just should write x! f(x) = x! for example 0 is bigger than x and less/equal than 1 so f(0) = 0

and for all the x that are more than 1 we have -1...for example 2 is more than z (2>1) so f(2) = -1 , and f(3) = -1 , so for all the Ns that Ns are more than 1, f(N) = -1

Answer 16

ahh .. wait.. so if x is less than or equal to -1.. f(x) = x^2+4x..? is that it..?

Answer 17

yes

Answer 18

aaahhh ok wait

Answer 19

there is a given number.. its -4 so those ifs are the clue on which equation you will use to substitute the -4..?

Answer 20

yes :) we should find where is -4 , is more than 1 or is less/equal than -1 or is between -1 and 1 ? and then use the correct function :)

Answer 21

got it?

Answer 22

hahaha.. FINALLY.. hwahhaha

Answer 23

got it.. one last question.. how will i read this.. if −1 < x ≤ 1..?

Answer 24

English is not really my mother-language and i don't know in english countries how do they read this :D
but i think we should read this: if x is bigger than -1 and it's less or equal than 1.

Answer 25

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Answer 26

hwahha.. same my mother-language is not english .. im a filipino.. haha.. maybe thats how it should be read. haha tnx again..

Answer 27

you're welcome ;)

Answer 28

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Answer 29

ok @factor :D i'll join.i bumped my practicing studio too.i'll practice LATEX again and then i will join your topic :)

Answer 30

@factor neeeh no deal i dont know what is latex..? haha

Answer 31

go to this topic to know :
http://openstudy.com/study#/groups/LaTeX%20Practicing!%20%3A)
you can learn how to write LaTeX in the tutorials.

Answer 32

ok @russeldano if you have given the aswers , you can close your question ;)

Answer 33

haha.. ok.. haha tnx again.. haha