Can someone please help me with a question?

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Can someone please help me with a question?

Mathematics
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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?

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Other answers:

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
your answer, is: \[g\left( x \right) = m\left( {x + 1} \right) + b = mx + m + b\] and we have completed your exercise
Wait, so what option would I choose? I'm confused.
the first option
Can you help me with another question?
ok!
when we make a reflection with respect to the x-axis, then we can write the new function g(x) as below: \[g\left( x \right) = - f\left( x \right)\]
So, how would I solve?
it is simple, you have to replace f(x) with its formula: \[g\left( x \right) = - f\left( x \right) = - \left( {{x^2} + 5} \right) = ...?\]
Would the answer be g(x)= -x^2+5?
not exactly, since when you cancel the parentheses, you get this: \[g\left( x \right) = - f\left( x \right) = - \left( {{x^2} + 5} \right) = - {x^2} - 5\]
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!
here we have to consider all points whose y-coordinate is less the y coordinate of the points which belong to the straight line
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
your line passes at points (-5,0) and (0,6), so its equation is: \[\frac{{y - 0}}{{6 - 0}} = \frac{{x + 5}}{{0 + 5}}\]
It actually passes at -6 and 5 though.
which can be simplified to this form: \[6x - 5y = - 30\]
So, what option would I choose?
please wait, I think that your line passes at points (-6,0) and (0,5), so its equation is: \[5x - 6y = - 30\]
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?
more explanation: the y-coordinate of the points of the shaded region has to be less than the y-coordinate of the point of the straight line, so we can write this: \[y \leqslant \frac{{5x - 30}}{6}\]
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.
the y-coordinates of the new function g(x) have to be six time greater than the respectively y-coordinate of the old function f(x)
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!
-7 means shifting down by 7 units furthermore, as we can see in your first exercise, x+3 means shifting to left
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

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