Question

Does this graph have any minimums or maximums?

Answer 1

min is -2 when x = -3

Answer 2

looks like no max but we only see part of the graph

Answer 3

(-3, -2) is the minumum but no maximum

Answer 4

thats the whole graph i think it just keeps going

Answer 5

thanks!

Answer 6

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

Answer 7

there is no minium

Answer 8

who's to say it continues in a postitve direction?

Answer 9

There is domain and range both of which have a minimum value in this case,

Answer 10

wow im confused

Answer 11

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

Answer 12

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

Answer 13

hey gianfranco is what satellite said earlier true?

Answer 14

yes. this is a never ending source of confusion. the minimum is the output, not the input.

Answer 15

Of course, satellite is always right.

Answer 16

for example, if the function is \[f(x)=x^2-5\] the minimum value is -5

Answer 17

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

Answer 18

and no, i am often wrong!

Answer 19

ok im going to take your word on it but what ecin is saying is reasonable too

Answer 20

ah so what should i put as the answer??

Answer 21

I think it is better to acknowledge the point at which the graph takes a minimum vale which includses voth domain and range,

Answer 22

value

Answer 23

There is a minimum. There is no max because the graph appears to be cut off and 'continues' though we can't see it.

Answer 24

um we kinda alread acknowledged that lol

Answer 25

there's no minimum

Answer 26

jesus

Answer 27

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

Answer 28

oh. wait i didn't see the equation sorry

Answer 29

I just saw the graph lol

Answer 30

ecin there was no equation

Answer 31

then there's no minimum

Answer 32

you don't know what happens outside. You are garanteed a min domain x-coordinate

Answer 33

well given that the graph doesnt show which way it continues i think (-3,-2) is correct

Answer 34

that's my point exactly

Answer 35

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,

Answer 36

picture a capacitor graph before it discharges

Answer 37

you don't konw the lim x->inf

Answer 38

gian you are right and based on http://tutorial.math.lamar.edu/Classes/CalcI/MinMaxValues.aspx example four the minimum is probably x=-3

Answer 39

Definitely not probably I can assure you :)

Answer 40

ok well should i pout x=-3 or a coordinate?

Answer 41

*put

Answer 42

in example 4 . the x doesn't increase anymore showing you tahat theres o more inclrease or decrease

Answer 43

do what you want. I'm tired of arguing.

Answer 44

Coordinate but remember to state that it is a definite minimum, and importantly also state that there is no maximum.

Answer 45

what do you mean by definite minimum? and ok

Answer 46

he means i'm wrong, where i stand on my belief i'm right

Answer 47

Well Ecin, the question doesn't ask about extemum, os the point would at least be considered relative minimum.

Answer 48

it's a local min for sure

Answer 49

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 .

Answer 50

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

Answer 51

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.