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the new function g(x) has to be equal to the old function f at point x+1

What does that mean?

in formula, my statements means:
g(x)=f(x+1)

So kind of like for example y= mx+b?

in that case, we can write this:
g(x9=m(x+1)+b

oops..
g(x)=m(x+1)+b

By the way, sorry if I seem slow with this, I'm just really bad with math.

no worries! :)

So, g(x)=m(x+1)+b

yes!

How would I solve the answer with that?

I think you have to do the multiplication, like below:
g(x)=mx+m+b

How do I do the multiplication with this equation?

we can do the multiplication above using the distributive property of multiplication over addition

I think I remember how to do that, is there a formula?

So, (sorry to ask again) what numbers would be put in?

the general formula, is:
\[\left( {a + b} \right)c = ac + bc,\quad \forall a,b,c \in \mathbb{R}\]

you have to know the values of the coefficients m and b

I feel really stupid to keep asking for help, but how would I find the coefficients?

you can retrieve the value of those coefficients, from the text of your exercise

The only number I had from the exercise is "1"

in that case your exercise is not a numeric exercise

Hang on, let me repost the question

ok!

Okay, that's the question

Wait, so what option would I choose? I'm confused.

the first option

Can you help me with another question?

ok!

So, how would I solve?

Would the answer be g(x)= -x^2+5?

I'm confused D:

every term inside the parentheses change its sign

so we can write this:
\[ - \left( {{x^2} + 5} \right) = - {x^2} - 5\]

So, the first option?

yes!

Can you help me with another one?

ok!

Let me guess, it's the first option right?

Or is it another one?

please wait, first we have to write the equation of the straight line

Okay, so how would we do that?

I know that the line is at -6 and 5

It actually passes at -6 and 5 though.

which can be simplified to this form:
\[6x - 5y = - 30\]

So, what option would I choose?

So, would it be C or D?

so the shaded part of cartesian plane is represented by this inequality:
\[5x - 6y \geqslant - 30\]

So, D?

Can you help me with another one please?

Can you help me with this question?

Please?

we can write this:
\[g\left( x \right) = 5\left( { - 7{x^2}} \right) + 5 = 5f\left( x \right) + 5\]

I think the answer is D

yes! correct!

Yay! Can you help me with another one please?

ok!

Okay, that's the question.

So, would the answer be C?

no, I meant six as a factor

Oh, so would it be A? Because it has multiplication?

correct!

Can you help me with another one?

please wait, since another student has requested my help

It's a quick question though

ok!

So, would it be C?

Oh, wait, B?

no, since the vertical shift is by 7 units down and the horizontal shift is by 3 units left

So, B?

correct! it is option B

Do you think you could help me with another?

yes! please wait