How Do You Transform the Graph of f(x) = 3x - 2 to g(x) = 6x + 1?

[Peter G.]

The function of f is given by f(x) = 3x - 2, where x is part of a set of real numbers. Sketch the graph of f. Find a combination of geometrical transformations of which, when applied to the graph of f will give the graph of g(x) = 6x + 1

At a first glance I thought: Stretch by a scale factor of 2 and translate by a vector of (0 2)

But the book's answer tell me otherwise: Stretch by factor 2 but a translation of vector (0 5) Can anyone help me please?

Thanks,
Peter G.

 

[tiny-tim]

Hi Peter!

The function of f is given by f(x) = 3x - 2, where x is part of a set of real numbers. Sketch the graph of f. Find a combination of geometrical transformations of which, when applied to the graph of f will give the graph of g(x) = 6x + 1

At a first glance I thought: Stretch by a scale factor of 2 and translate by a vector of (0 2)

How did you get (0,2) ?

 

[Peter G.]

Oh, wait, I think I got it!

If I do f (2x) I get 6x - 4, thus, if x = 2:

y = 8

while, for g (x) when x = 2 we get 13

13 - 8 = 5.

Is that it?

 

[tiny-tim]

yeeees

If I do f (2x) I get 6x - 4

why not just do 6x - 4 + 5 = 6x + 1 ?

 

[Peter G.]

Cool! Thanks!

Oh, you mean, once I do f (2x) to find it is +5 I could do:

6x - 4 + x = 6x + 1
6x - 6x + x = 1 - (-4)
x = 5

?

 

[tiny-tim]

6x - 4 + x = 6x + 1
6x - 6x + x = 1 - (-4)
x = 5

You seem to be using x to mean two different things.

Start again …

the given graph is (x,3x - 2) …

stretch it to get (x,6x - 4) …

then add (0,5) to get (x,6x - 1)

 

[Peter G.]

Ok, thanks again Tiny Tim

 

[Peter G.]

Oh, sorry Tiny-Tim, if you don't mind...

The functions f and g are defined for all real numbers by f (x) = -x² and g(x) x² + 2x + 8

a) Express g (x) in the format (x+a)² + b where a and b are constants:

Ok, this one was ok, (x+1)² + 7

b) Describe two transformations, in detail and the order in which they be applied whereby the graph of g may be obtained from the graph of f

Well, the question asks for the order, and the answer given by the book was reflection in the x-axis followed by translation of -1,7

What I wrote however, was: translation of (-1,7) and then a reflection in the x axis, are both answers acceptable?

Thanks once again and I promise it will be the last question on these graphs :shy:
Peter G.

 

[tiny-tim]

Well, the question asks for the order, and the answer given by the book was reflection in the x-axis followed by translation of -1,7

What I wrote however, was: translation of (-1,7) and then a reflection in the x axis, are both answers acceptable?

No!

Have you drawn this?

If you do (-1,7) first, then you push the top of the curve well above the x-axis: so when you reflect in it, the bottom will be well below the x-axis.

(You could do a translation first, but that would need to push the curve down …

can you now see what it would need to be?)

 

[Peter G.]

Ah... yes... sorry, it was a stupid question I made because I didn't notice the effect it would have moving the curve vertically.

Thanks