C1 Transformations Maths Help

When doing transformations of reciprocal graphs, how do I find out the points where the graphs touch the x/y axis? I know how to transform the graphs, but i get stuck because i dont know where the intercepts are. Im doing the second question in the picture. Thanks in advance

(edited 8 years ago)

Reply 1

DylanJ42

18

Original post by doglover123

When doing transformations of reciprocal graphs, how do I find out the points where the graphs touch the x/y axis? I know how to transform the graphs, but i get stuck because i dont know where the intercepts are. Im doing the second question in the picture. Thanks in advance

I'm pretty sure the only point where that curve crosses the axis after any of those transformations (excluding a) ofc) is the point (0,0) gets transformed to

Reply 2

Zacken

22

Original post by doglover123

When doing transformations of reciprocal graphs, how do I find out the points where the graphs touch the x/y axis? I know how to transform the graphs, but i get stuck because i dont know where the intercepts are. Im doing the second question in the picture. Thanks in advance

x-axis: f(x) is 0 when x = 1 or x = 6.

Now, for example, (c) f(x+4) will be 0 whenever x+4 = 1 or x+4=5

(b) will be whenever f(x) - 4 = 0 which is when f(x) = 4 which is when x=4.

And you can apply the same principle to the other parts.

y-axis:

hits y-axis when x=0. so (a) f(0+1) = f(1) = 0
(b) f(0) - 4 = 2-4 = blah blah blah

apply the same principal to the other parts.

Edit: I didn't read the question properly and my answer is based on the first problem on the page. Sorry... the same thing should still apply, however.

------------------------------------------------------------

Answering the proper question

x-axis: f(x) = 0 when x=0. so for (b) f(x+1) = 0 when x+1 =0, i.e: x=-1
(c) 2f(x) = 0 when f(x) = 0, so x=0, etc...

In general, if you have a function

g(x) = 0

at

x_1

then your transformed function

h(x) = g(x + \alpha)

will cross the axis when

x+\alpha = x_1

or similarly for another transformation, such as

h(x) = g(\alpha x)

, then that's

\alpha x = x_1

.

y-axis:

Just plug x=0 in and you should get the point. E.g: (d) x= 0 gives f(0) - 2= 0 -2 = -2.

(edited 8 years ago)

Reply 3

tinkerbella~

13

Original post by Zacken

x-axis: f(x) is 0 when x = 1 or x = 6.

Now, for example, (c) f(x+4) will be 0 whenever x+4 = 1 or x+4=5

(b) will be whenever f(x) - 4 = 0 which is when f(x) = 4 which is when x=4.

And you can apply the same principle to the other parts.

y-axis:

hits y-axis when x=0. so (a) f(0+1) = f(1) = 0
(b) f(0) - 4 = 2-4 = blah blah blah

apply the same principal to the other parts.