Question

I just want to get this done so I can sleep. ):
Please help):

Answer 1

Question 1-
Identify the domain of the equation y = x2 − 6x + 1. (1 point)

x ≤ 3
x ≥ −8
x ≥ −2
All real numbers

Question 2-
Functions f(x) and g(x) are shown below:
f(x) = x2
g(x) = x 2 + 8x + 16

In which direction and by how many units should f(x) be shifted to obtain g(x)? (1 point)

Left by 4 units
Right by 4 units
Left by 8 units
Right by 8 units

Answer 2

@Luigi0210 @sleepyjess @maryfitzgerald14 @jim_thompson5910 @Kainui @El_Arrow

Answer 3

So for question one, keep in mind that the domain is essentially all the numbers that you can plug in to an equation, and get a valid number out.

So for that, you can go ahead and just try some different numbers.

Say, x= 2 (Which is less than 3).

Plug this in you get ((3)^2 -6(3) +1)

Which is just 9-18+1
which is -8, which is a real number.

Answer 4

You can try for other numbers that would satisfy the others, and find that you get a real number back every time (feel free to go ahead and plug some examples in like I did). You'll find that all numbers you put in can be squared, all numbers can be multiplied by 3, and all numbers can be added and subtracted

Answer 5

Thus the domain is all real numbers.

Answer 6

Thank you!(: Also thank you for explaining it! Can you explain the second one also?

Answer 7

Sure. So, there are 2 "Basic" things you can do to an equation, you can move it up/down, and you can move it left/right.

Answer 8

Moving it up/down is pretty simple. You just add numbers to the equation to shift the whole thing (think y=mx+b. Adding b just moving y=mx up to b, and subtracting b just moves it down to b).

Answer 9

Moving it left and right is probably a bit less intuitive.

Answer 10

But essentially, what you want to do it subtract from just the "x" portion of the equation.

Answer 11

By adding or subtracting from just the "x" part, you are essentially telling the function "Use the x from somewhere else on the number line"

Answer 12

Which is going to move your x left or right.

Answer 13

So for the equation, f(x) + x^2

Answer 14

You're just adding or subtracting from the x part.

Answer 15

So it's going to be g(x) = (x+h)^2

Answer 16

Now, you might be thinking "that doesn't look like any of our options" but keep in mind, that you can expand that to be

x^2 +2h +16

Answer 17

or my bad, x^2 +2h + h^2

Answer 18

So from there, it should be obvious that 8 or -8 is not going to be the answer, right? Cause that'd leave you with something like

x^2 + 16 + 64 which looks nothing like our original equation

Answer 19

x^2 +16x +64*

Answer 20

So it's got to be either h=4 or h=-4

Answer 21

It's going to be h=4 if you just work it out. So let's think about how that affects the equation

Answer 22

So now you've got to think "What does adding 4 to x tell the equation to do?"

Answer 23

Well, it's telling the equation to use numbers for x from 4 in the past, essentially, right?

Answer 24

yes

Answer 25

So that's going to move the equation 4 units to the left.

Answer 26

Thank you so much for helping me understand(:

Answer 27

Yep. You understand the thought process right? Think you could solve this type of problem on a test?