Liv1234
  • Liv1234
Can someone please help me with a question?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Liv1234
  • Liv1234
Michele_Laino
  • Michele_Laino
the new function g(x) has to be equal to the old function f at point x+1
Liv1234
  • Liv1234
What does that mean?

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More answers

Michele_Laino
  • Michele_Laino
in formula, my statements means: g(x)=f(x+1)
Liv1234
  • Liv1234
So kind of like for example y= mx+b?
Michele_Laino
  • Michele_Laino
in that case, we can write this: g(x9=m(x+1)+b
Michele_Laino
  • Michele_Laino
oops.. g(x)=m(x+1)+b
Liv1234
  • Liv1234
By the way, sorry if I seem slow with this, I'm just really bad with math.
Michele_Laino
  • Michele_Laino
no worries! :)
Liv1234
  • Liv1234
So, g(x)=m(x+1)+b
Michele_Laino
  • Michele_Laino
yes!
Liv1234
  • Liv1234
How would I solve the answer with that?
Michele_Laino
  • Michele_Laino
I think you have to do the multiplication, like below: g(x)=mx+m+b
Liv1234
  • Liv1234
How do I do the multiplication with this equation?
Michele_Laino
  • Michele_Laino
we can do the multiplication above using the distributive property of multiplication over addition
Liv1234
  • Liv1234
I think I remember how to do that, is there a formula?
Liv1234
  • Liv1234
So, (sorry to ask again) what numbers would be put in?
Michele_Laino
  • Michele_Laino
the general formula, is: \[\left( {a + b} \right)c = ac + bc,\quad \forall a,b,c \in \mathbb{R}\]
Michele_Laino
  • Michele_Laino
you have to know the values of the coefficients m and b
Liv1234
  • Liv1234
I feel really stupid to keep asking for help, but how would I find the coefficients?
Michele_Laino
  • Michele_Laino
you can retrieve the value of those coefficients, from the text of your exercise
Liv1234
  • Liv1234
The only number I had from the exercise is "1"
Michele_Laino
  • Michele_Laino
in that case your exercise is not a numeric exercise
Liv1234
  • Liv1234
Hang on, let me repost the question
Michele_Laino
  • Michele_Laino
ok!
Liv1234
  • Liv1234
Liv1234
  • Liv1234
Okay, that's the question
Michele_Laino
  • Michele_Laino
your answer, is: \[g\left( x \right) = m\left( {x + 1} \right) + b = mx + m + b\] and we have completed your exercise
Liv1234
  • Liv1234
Wait, so what option would I choose? I'm confused.
Michele_Laino
  • Michele_Laino
the first option
Liv1234
  • Liv1234
Can you help me with another question?
Michele_Laino
  • Michele_Laino
ok!
Liv1234
  • Liv1234
Michele_Laino
  • Michele_Laino
when we make a reflection with respect to the x-axis, then we can write the new function g(x) as below: \[g\left( x \right) = - f\left( x \right)\]
Liv1234
  • Liv1234
So, how would I solve?
Michele_Laino
  • Michele_Laino
it is simple, you have to replace f(x) with its formula: \[g\left( x \right) = - f\left( x \right) = - \left( {{x^2} + 5} \right) = ...?\]
Liv1234
  • Liv1234
Would the answer be g(x)= -x^2+5?
Michele_Laino
  • Michele_Laino
not exactly, since when you cancel the parentheses, you get this: \[g\left( x \right) = - f\left( x \right) = - \left( {{x^2} + 5} \right) = - {x^2} - 5\]
Liv1234
  • Liv1234
I'm confused D:
Michele_Laino
  • Michele_Laino
every term inside the parentheses change its sign
Michele_Laino
  • Michele_Laino
so we can write this: \[ - \left( {{x^2} + 5} \right) = - {x^2} - 5\]
Liv1234
  • Liv1234
So, the first option?
Michele_Laino
  • Michele_Laino
yes!
Liv1234
  • Liv1234
Can you help me with another one?
Michele_Laino
  • Michele_Laino
ok!
Liv1234
  • Liv1234
Michele_Laino
  • Michele_Laino
here we have to consider all points whose y-coordinate is less the y coordinate of the points which belong to the straight line
Liv1234
  • Liv1234
Let me guess, it's the first option right?
Liv1234
  • Liv1234
Or is it another one?
Michele_Laino
  • Michele_Laino
please wait, first we have to write the equation of the straight line
Liv1234
  • Liv1234
Okay, so how would we do that?
Liv1234
  • Liv1234
I know that the line is at -6 and 5
Michele_Laino
  • Michele_Laino
your line passes at points (-5,0) and (0,6), so its equation is: \[\frac{{y - 0}}{{6 - 0}} = \frac{{x + 5}}{{0 + 5}}\]
Liv1234
  • Liv1234
It actually passes at -6 and 5 though.
Michele_Laino
  • Michele_Laino
which can be simplified to this form: \[6x - 5y = - 30\]
Liv1234
  • Liv1234
So, what option would I choose?
Michele_Laino
  • Michele_Laino
please wait, I think that your line passes at points (-6,0) and (0,5), so its equation is: \[5x - 6y = - 30\]
Liv1234
  • Liv1234
So, would it be C or D?
Michele_Laino
  • Michele_Laino
so the shaded part of cartesian plane is represented by this inequality: \[5x - 6y \geqslant - 30\]
Liv1234
  • Liv1234
So, D?
Liv1234
  • Liv1234
Can you help me with another one please?
Michele_Laino
  • Michele_Laino
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: \[y \leqslant \frac{{5x - 30}}{6}\]
Liv1234
  • Liv1234
Can you help me with this question?
Liv1234
  • Liv1234
Please?
Michele_Laino
  • Michele_Laino
we can write this: \[g\left( x \right) = 5\left( { - 7{x^2}} \right) + 5 = 5f\left( x \right) + 5\]
Liv1234
  • Liv1234
I think the answer is D
Michele_Laino
  • Michele_Laino
yes! correct!
Liv1234
  • Liv1234
Yay! Can you help me with another one please?
Michele_Laino
  • Michele_Laino
ok!
Liv1234
  • Liv1234
Liv1234
  • Liv1234
Okay, that's the question.
Michele_Laino
  • Michele_Laino
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)
Liv1234
  • Liv1234
So, would the answer be C?
Michele_Laino
  • Michele_Laino
no, I meant six as a factor
Liv1234
  • Liv1234
Oh, so would it be A? Because it has multiplication?
Michele_Laino
  • Michele_Laino
correct!
Liv1234
  • Liv1234
Can you help me with another one?
Michele_Laino
  • Michele_Laino
please wait, since another student has requested my help
Liv1234
  • Liv1234
It's a quick question though
Michele_Laino
  • Michele_Laino
ok!
Liv1234
  • Liv1234
Michele_Laino
  • Michele_Laino
-7 means shifting down by 7 units furthermore, as we can see in your first exercise, x+3 means shifting to left
Liv1234
  • Liv1234
So, would it be C?
Liv1234
  • Liv1234
Oh, wait, B?
Michele_Laino
  • Michele_Laino
no, since the vertical shift is by 7 units down and the horizontal shift is by 3 units left
Liv1234
  • Liv1234
So, B?
Michele_Laino
  • Michele_Laino
correct! it is option B
Liv1234
  • Liv1234
Do you think you could help me with another?
Michele_Laino
  • Michele_Laino
yes! please wait

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