Question

Compare the functions shown below:

Answer 1

https://prnt.sc/hd2e66
Which function has the smallest minimum y-value?
f(x)
g(x)
h(x)
Both f(x) and g(x) have the same minimum y-value.

Answer 2

@Shadow @Vocaloid

Answer 3

What are the different functions?

Answer 4

Oh, wait, I'm stupid.. xD

Answer 5

LOL It's fine x'D

Answer 6

Aah xD Did you get your question yet, or are you still working on it?

Answer 7

Still working on it :D

Answer 8

I gotchyu. What all have you done so far? Like, have you came to any conclusions yet?

Answer 9

Not really :| I tried using mathway, desmos

Answer 10

f(x) is a sin function, and the "parent" or default sin(x) function normally has a minimum of -1

except it's been multiplied by -4, which changes the amplitude so the minimum value of -4(sin(x)) is -4

the (2x-pi) inside the sin function only translates/stretches the function horizontally so these transformations don't change the minimum value

and the -1 at the end shifts the entire graph down, making the minimum -5

Answer 11

the minimum of g(x) is straightforward, it's just the smallest value of g(x) in the table, which is -3

Answer 12

and for h(x), normally the x^2 has a minimum of 0, and in this case the -2 inside the parentheses does not change the minimum since this is a horizontal transformation, and the +4 at the end shifts the entire function up by 4, making the minimum 4

Answer 13

Ah okie, I see now