Transformations of functions help

[Trail_Builder]

bascially, my teacher rushed us through transformations of functions in an hour, and didnt have time to go throuhg it all so i need some expalnations from you guys please

(you don't have to do it for me, just tell me where to go, thnx)

1.) The curve with equation y = x^2 - 2x - 3 reflected in the y-axis. Find the equation of this new curve.

right, i know that when y=f(x) that to reflect in y-axis I do y=f(-x).

so, to answer the question, do i simply stick a - sign in front of all the x? leaving y = -x^2 + 2x - 3 ? but then, let's say i changed the question to the x-axis (i know when y=f(x) to reflect in x-axis you do y=-f(x) ) i am now more confused because i would guess to also stick minus in front again ? which i know i can't do the same.

can someone please explain what to do, thnx

2.) Describe fully the sequence of two transformations that maps the graph of y = sinx onto the graph of y=3sin2x

i know how to do the bit relating to 3, which is 'multiply the y-value by 3', but i not sure how to do the transformation relating to 2, can you advise please. thnx

3.) (not sure how it relates to transformations of functions but its on the list of related qus) The depth, D metres, of the water at the end of a jetty in the afternoon can be modeled by this formula

D = 5.5 + Asin30(t - k)deg

where

t hours is the number of hours after midday
A and k are constants.

Yesterday the low tide was at 3pm
The depth of wter at low tide was 3.5m

Find the value of A and k

is it as simple as subbing the values in? because that somehow seems to easy and not related to transformation of functions?

thnx

hope you can help will these and please explain rather than tell me answer, thnx a bunch

 

[dontdisturbmycircles]

Do you have a graphing calculator? You could test #1 for yourself and see if it works. For #2, if a is a positive number, the graph of $$f(\frac{x}{a})$$ is the graph of f(x) stretched horizontally by a factor of a and the graph of f(ax) is the graph of f(x) compressed by a factor of a.

More info for #1, let's say we are given f(x)=2x+4

f(-x)=-2x+4
-f(x)=-2x-4

The best way to understand transformations is to pick up your graphing calculator, punch in y=x+4, then try y=-x+4, then try y=$$\frac{x}{2}$$+4, then try y==$$\frac{x}{2}$$+8, etc. Try to understand why it is happening.

 

[Trail_Builder]

thnx buddy, yeh i have a an uber sweet calculator, cost like 70 quid hehe, so yeh it can do graphs, ill have a play at school tomoz, thnx

 

[HallsofIvy]

bascially, my teacher rushed us through transformations of functions in an hour, and didnt have time to go throuhg it all so i need some expalnations from you guys please

(you don't have to do it for me, just tell me where to go, thnx)

1.) The curve with equation y = x^2 - 2x - 3 reflected in the y-axis. Find the equation of this new curve.

right, i know that when y=f(x) that to reflect in y-axis I do y=f(-x).

so, to answer the question, do i simply stick a - sign in front of all the x? leaving y = -x^2 + 2x - 3 ? but then, let's say i changed the question to the x-axis (i know when y=f(x) to reflect in x-axis you do y=-f(x) ) i am now more confused because i would guess to also stick minus in front again ? which i know i can't do the same.

can someone please explain what to do, thnx

surely your algebra is better than that! f(-x) means that x is replaced with -x so that, for example, x² become (-x)². That is NOT -x²! y= (-x)²+ 2(-x)- 3= what?

2.) Describe fully the sequence of two transformations that maps the graph of y = sinx onto the graph of y=3sin2x

i know how to do the bit relating to 3, which is 'multiply the y-value by 3', but i not sure how to do the transformation relating to 2, can you advise please. thnx

I would not say 'multiply the y-value by 3' but rather 'stretch the graph vertically by 3': a "transformation" is geometric. As for the 2, your "base" equation is y= sin(x). If you think of y= sin(2x)= sin(x') then x'= 2x so x= x'/2. The "old" x value is divided by 2. Geometrically, the graph is "squeezed" horizontally by a factor of 1/2.

Are you related to "TheMatador"? see
https://www.physicsforums.com/showthread.php?t=152054

3.) (not sure how it relates to transformations of functions but its on the list of related qus) The depth, D metres, of the water at the end of a jetty in the afternoon can be modeled by this formula

D = 5.5 + Asin30(t - k)deg

where

t hours is the number of hours after midday
A and k are constants.

Yesterday the low tide was at 3pm
The depth of wter at low tide was 3.5m

Find the value of A and k

is it as simple as subbing the values in? because that somehow seems to easy and not related to transformation of functions?

thnx

hope you can help will these and please explain rather than tell me answer, thnx a bunch

Yes, it is that easy! Substitute the values given and you will have two equations to solve for A and k.