Question

Step-fuctions:

Evaluate the function for the indicated values:

g(x)=2[[x]]

a) g(-3)
b) g(0.25)
c) g(9.5)
d) g(11/3)

Wouldn't I plug in the greatest integer less than the value I'm plugging in? That's what my teacher said. So, for example, wouldn't I plug in -3 for a, 0 for b, 9 for c and 3 for d?

Answer 1

@jim_thompson5910 can you help me please?

Answer 2

[[x]] is the greatest integer function which means you round down to the nearest whole number

examples:

[[0.2]] = 0
[[6.8]] = 6
[[-2.1]] = -3

Basically wherever you are on the number line, you move left to the nearest integer. If you are already at an integer, you stay where you are.

Answer 3

I'll do part b


g(x)=2[[x]]

g(0.25)=2[[0.25]]

g(0.25)=2*0

g(0.25)=0

Answer 4

so it looks like you have it correct

Answer 5

Ok, so the answers would be:
a) -3
b) 0
c) 9
d) 3

Correct? Because if that is, then I have one more question.

Answer 6

you are forgetting about the 2 hanging out front

Answer 7

the function is NOT g(x) = [[x]]

it is g(x) = 2[[x]]

Answer 8

Ohhh, so I have to multiply it by 2. Alright, got it. But I have one more question.

Answer 9

ok go ahead

Answer 10

The function is g(x)=3[[x-2]]+5, and the given values are:
a) g(1/8)
b) g(9)
c) g(-4)
d) g(3/2)

I did the right thing but I'm still not getting the right answers. I know because I checked the answers in the back of my book but they're not correct.

Answer 11

what answers are you getting

Answer 12

Oops, I gave the wrong values for a-d.
a) g(-2.7)
b) g(-1)
c) g(0.8)
d) g(14.5)

Sorry about that. And for the first one I got.... -7. The second one I got -4, the third one I got -1 and for the last one I got 41.

Answer 13

Actually, all of them are right but the first one. Idk what I'm doing wrong in the first one.

Answer 14

g(x)=3[[x-2]]+5

g(-2.7)=3[[-2.7-2]]+5

g(-2.7)=3[[-4.7]]+5

g(-2.7)=3*(-5)+5 ... round down

g(-2.7)=-15+5

g(-2.7)=-10

Answer 15

you do NOT do this

g(x)=3[[x-2]]+5

g(-2.7)=3[[-2.7-2]]+5

g(-2.7)=3[[-4.7]]+5

g(-2.7)=3*(-4)+5

g(-2.7)=-12+5

g(-2.7)=-7

this is all wrong because -4.7 should round down to -5 and not to -4

Answer 16

Ohhhh ok. So if I wanted to plug in the greatest integer less than -2.7, I'd plug in -3?

Answer 17

that is if you had [[x]] and you plugged in x = -2.7

but you have [[x-2]]

Answer 18

[[x]] means...

wherever you are on the number line, you move left to the nearest integer. If you are already at an integer, you stay where you are.

Answer 19

Right, so was I wrong about the -3? Cuz when I plugged in -3 for x in g(-2.7)=3[[-3-2]]+5, I got -10, which is correct.

Answer 20

[[x]] is also known as the floor function

because you go to the "floor", which basically the closest whole number

Answer 21

well it is coincidental that [[-3-2]] = [[-2.7 - 2]]

the error you made could produce a false answer down the road

Answer 22

[[-3-2]] = [[-5]] = -5

[[-2.7-2]] = [[-4.7]] = -5

they lead to the same output, but they aren't the same

Answer 23

Oh okay. That makes sense. I'll practice some more to get the hang of it. It's still a bit confusing. We just learned this today but I'll ask my teacher for help too.

Answer 24

ok sounds good

Answer 25

Thank you :)

Answer 26

you're welcome