Question

Can someone please help me with a question?

Answer 1

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

Answer 2

What does that mean?

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

no worries! :)

Answer 9

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

Answer 10

yes!

Answer 11

How would I solve the answer with that?

Answer 12

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

Answer 13

How do I do the multiplication with this equation?

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

in that case your exercise is not a numeric exercise

Answer 23

Hang on, let me repost the question

Answer 24

ok!

Answer 25

Okay, that's the question

Answer 26

your answer, is:
\[g\left( x \right) = m\left( {x + 1} \right) + b = mx + m + b\]
and we have completed your exercise

Answer 27

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

Answer 28

the first option

Answer 29

Can you help me with another question?

Answer 30

ok!

Answer 31

when we make a reflection with respect to the x-axis, then we can write the new function g(x) as below:
\[g\left( x \right) = - f\left( x \right)\]

Answer 32

So, how would I solve?

Answer 33

it is simple, you have to replace f(x) with its formula:
\[g\left( x \right) = - f\left( x \right) = - \left( {{x^2} + 5} \right) = ...?\]

Answer 34

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

Answer 35

not exactly, since when you cancel the parentheses, you get this:
\[g\left( x \right) = - f\left( x \right) = - \left( {{x^2} + 5} \right) = - {x^2} - 5\]

Answer 36

I'm confused D:

Answer 37

every term inside the parentheses change its sign

Answer 38

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

Answer 39

So, the first option?

Answer 40

yes!

Answer 41

Can you help me with another one?

Answer 42

ok!

Answer 43

here we have to consider all points whose y-coordinate is less the y coordinate of the points which belong to the straight line

Answer 44

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

Answer 45

Or is it another one?

Answer 46

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

Answer 47

Okay, so how would we do that?

Answer 48

I know that the line is at -6 and 5

Answer 49

your line passes at points (-5,0) and (0,6), so its equation is:
\[\frac{{y - 0}}{{6 - 0}} = \frac{{x + 5}}{{0 + 5}}\]

Answer 50

It actually passes at -6 and 5 though.

Answer 51

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

Answer 52

So, what option would I choose?

Answer 53

please wait, I think that your line passes at points (-6,0) and (0,5), so its equation is:
\[5x - 6y = - 30\]

Answer 54

So, would it be C or D?

Answer 55

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

Answer 56

So, D?

Answer 57

Can you help me with another one please?

Answer 58

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:
\[y \leqslant \frac{{5x - 30}}{6}\]

Answer 59

Can you help me with this question?

Answer 60

Please?

Answer 61

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

Answer 62

I think the answer is D

Answer 63

yes! correct!

Answer 64

Yay! Can you help me with another one please?

Answer 65

ok!

Answer 66

Okay, that's the question.

Answer 67

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)

Answer 68

So, would the answer be C?

Answer 69

no, I meant six as a factor

Answer 70

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

Answer 71

correct!

Answer 72

Can you help me with another one?

Answer 73

please wait, since another student has requested my help

Answer 74

It's a quick question though

Answer 75

ok!

Answer 76

-7 means shifting down by 7 units
furthermore, as we can see in your first exercise, x+3 means shifting to left

Answer 77

So, would it be C?

Answer 78

Oh, wait, B?

Answer 79

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

Answer 80

So, B?

Answer 81

correct! it is option B

Answer 82

Do you think you could help me with another?

Answer 83

yes! please wait