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min is -2 when x = -3
looks like no max but we only see part of the graph
(-3, -2) is the minumum but no maximum
thats the whole graph i think it just keeps going
hold the phone. minimum means minimum value that y takes on. the minimum is not a coordinate. the minimum is a number. in this case it is -2
there is no minium
who's to say it continues in a postitve direction?
There is domain and range both of which have a minimum value in this case,
wow im confused
the only information you know is that if it is a function x=-3 is the beggining of the domain but yo udon't have any range info
This graph represents a function of x. The domain of a function is all permissable values of x. The range, all permissable values of y Hence minimum value of x = -3 and minimum value oy y = -2
hey gianfranco is what satellite said earlier true?
yes. this is a never ending source of confusion. the minimum is the output, not the input.
Of course, satellite is always right.
for example, if the function is \[f(x)=x^2-5\] the minimum value is -5
the fact that this function takes on the value of -5 when x = 0 does not make the minimum (0,-5) the minimum is a number, not a coordinate
and no, i am often wrong!
ok im going to take your word on it but what ecin is saying is reasonable too
ah so what should i put as the answer??
I think it is better to acknowledge the point at which the graph takes a minimum vale which includses voth domain and range,
There is a minimum. There is no max because the graph appears to be cut off and 'continues' though we can't see it.
um we kinda alread acknowledged that lol
there's no minimum
f(x) = x^2 -5 and it is said the minimum value is =-5 and to be clear you are saying the minimum value is the y value then you are saying f(-5) = (-5)^2 -5 which is not true. this implies -5 = 20
oh. wait i didn't see the equation sorry
I just saw the graph lol
ecin there was no equation
then there's no minimum
you don't know what happens outside. You are garanteed a min domain x-coordinate
well given that the graph doesnt show which way it continues i think (-3,-2) is correct
that's my point exactly
Look at the graph Smurfy the dot at the left hand side implies there ore no lower points on the graph in terms of numerical value, so give both x and y values for sheer safety :) The fact that there is no point on the right of the graph implies it goes on to infinity,
picture a capacitor graph before it discharges
you don't konw the lim x->inf
gian you are right and based on http://tutorial.math.lamar.edu/Classes/CalcI/MinMaxValues.aspx example four the minimum is probably x=-3
Definitely not probably I can assure you :)
ok well should i pout x=-3 or a coordinate?
in example 4 . the x doesn't increase anymore showing you tahat theres o more inclrease or decrease
do what you want. I'm tired of arguing.
Coordinate but remember to state that it is a definite minimum, and importantly also state that there is no maximum.
what do you mean by definite minimum? and ok
he means i'm wrong, where i stand on my belief i'm right
Well Ecin, the question doesn't ask about extemum, os the point would at least be considered relative minimum.
it's a local min for sure
This is getting a little heavy. Look at the graph. It is not complicated. It shows that the graph does not extend beneath the coordinate (-3, -2) and also it does not 'appear' to have a resting place in the first quadrant .
the minimum value means the minimum output, not the minimum input. if your domain is all real numbers then there is no minimum input. so say that the minimum value of \[f(x)=x^2-5\] is -5 means this is the smallest output you can get. it does not say that the minimum possible value of x is -5, nor does it say what \[f(-5)\] is
if you are taking calc you will frequently have to find the maximum or minimum value of a function. to do this you will probably have to find the value of x that gives it to you. say the minimum values occurs when x = 7. that does not mean the minimum value is 7. that means the minimum value is f(7) whatever that may be.