Question

Compare the functions below:


f(x) = −3 sin(x − π) + 2 g(x)

x y
0 8
1 3
2 0
3 −1
4 0
5 3
6 8
h(x) = (x + 7)2 − 1


Which function has the smallest minimum?

Answer 1

@Directrix @mathmale

Answer 2

Please help me @Directrix or @mathmale

Answer 3

@Directrix @agent0smith

Answer 4

is there supposed to be something for g(x)

Answer 5

its that table

Answer 6

Please help

Answer 7

@jim_thompson5910

Answer 8

Couldn't you graph the two given equations f(x) and h(x) first, then compare the smaller minimum from f(x) and h(x) with the lowest point in the table of g(x).

Answer 9

The minimum of h(x) is -7 correct?

Answer 10

It's \[h(x) = (x + 7)^2 − 1\] right?

Answer 11

yes

Answer 12

Yes the minimum is -7

Answer 13

Do you know how to find the minimum for the sin function f(x)?

Answer 14

Ok, and the minimum of g(x) is 0?

Answer 15

No I dont

Answer 16

Do you know what the amplitude is?

Answer 17

Yes. The distance between the minimum and maximum?

Answer 18

Yes. In sinusoidal equations such as this it's the coefficient before the sin/cos. It's the 3

Answer 19

So what does that mean for the minimum?

Answer 20

Is it -1?

Answer 21

Yes the minimum is 1 do you understand that?

Answer 22

1 or -1?

Answer 23

Ok. The amplitude on a normal graph without vertical shifts (for example the +2 in this problem), for example 3sinx is 3. That means the maximum is 3 and the minimum is negative 3. Now that the graph is shifted up +2, the minimum is also shifted from up.

Answer 24

Ok. I really need to gert this done, so g(x) is the answer?

Answer 25

Both f(x) and g(x) have minimum of -1

Answer 26

Thats not an option

Answer 27

I think they all have a minimum of -1 cause i just graphed them all

Answer 28

Yeah they all do

Answer 29

yeah you're right

Answer 30

h(x) has a minimum of x = 7 but y=-1, sorry confusion there