Question

Compare the functions shown below:
f(x) = 2 sin (3x + π) − 2
g(x) = (x − 3)2 − 1
h(x)

x y
-2 3
-1 -2
0 -5
1 -6
2 -5
3 -2
4 3
Which function has the smallest minimum y-value?

Answer 1

@Abhisar

Answer 2

What's h(x)

Answer 3

h(x)

Answer 4

h(x) is the answer////

Answer 5

how?

Answer 6

What is the minimum of f(x)?

Answer 7

-2?

Answer 8

nope
its has the minimum when sin(3x+pi) is minimum

Answer 9

minimum of sin(3x+pi) is -1 ok?

Answer 10

but where did you get -1

Answer 11

any sin value can only exist between +1& -1 ok?

Answer 12

so +1 is maximum and -1 is minimum?

Answer 13

yes
so can you now tell the minimum of f(x)?

Answer 14

By studying the behavior of the sin graph. The graph is stretched by a vertical factor of 2 (meaning it oscillates from -2 to 2) and then by seeing that the -2 at end brings it down 2 units. So now it oscialltes from -4 to 0 so the min of that graph is -4, you forgot about the 2 in fron and the 2 being subtracted @amilapsn

https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=2sin(3x%2Bpi)-2

Answer 15

-1

Answer 16

The min of f(x) is -4

Answer 17

nope it's -4

Answer 18

no!!!!!!!!! im so confused

Answer 19

minf(x)=2(-1)-2, when plugging -1 to sin(3x+pi)

Answer 20

then the minimum of g(x) would be -2?

Answer 21

f(x):

https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=2sin(3x%2Bpi)-2

Min of -4

g(x)

https://www.google.com/search?q=(x+%E2%88%92+3)2+%E2%88%92+1&oq=(x+%E2%88%92+3)2+%E2%88%92+1&aqs=chrome..69i57&sourceid=chrome&es_sm=0&ie=UTF-8#q=(x+%E2%88%92+3)%5E2+%E2%88%92+1

Min of -1


h(x): By looking at the ordered pairs, the smallest y value is -6 so you can conclude that -6 is smaller than -4 and -1 (which are the mins of the other two functions)

Answer 22

no it's -1

Answer 23

how i thought you have to do 1(-1) - 1

Answer 24

am i not right?

Answer 25

no here we have to consider about,\[(x-3)^2\]

Answer 26

ok...

Answer 27

What do you think the minimum of \[(x-3)^2\]

Answer 28

-1

Answer 29

for any real x it will have a positive value except for...

Answer 30

x=3

Answer 31

ohhh ok

Answer 32

So what is the minimum of h(x)?

Answer 33

yeah thanks

Answer 34

but can i post another one for practice?

Answer 35

-6

Answer 36

OK..

Answer 37

Though this isn't the same problem, figured I'd post it here:

Answer 38

This was the prob:
Which function has the smallest minimum?
All three functions have the same minimum

f(x)

g(x)

h(x)

Answer 39

Ok, can you do it?