1. ## transforming linear function

Hi;
I need to transform the function f(x) = 2x + 3, four units up now I know how to do it just add 4 to the 3 but...

my issue is a transformed function has the expression f(x) = a(dx -h) + k so...

how do we know that 3 is vertical rather than horizontal I can only assume its because the brackets are missing in the original function ?

Thanks.

2. ## Re: transforming linear function

why would your transformed function be anything other than

$f(x) = 2x+7$ ?

3. ## Re: transforming linear function

its just a question that came up about transforming and about those brackets that I mentioned.

4. ## Re: transforming linear function

Originally Posted by anthonye
its just a question that came up about transforming and about those brackets that I mentioned.
so you want to transform the function $f(x) = a(dx - h)+k$ 3 units up?

$f(x)+3 = a(dx-h)+(k+3)$

5. ## Re: transforming linear function

yeah get that but what I mean is from the original function f(x) = 2x + 3 how do you know that the 3 is a vertical shift and not horizontal shift?

6. ## Re: transforming linear function

Originally Posted by anthonye
yeah get that but what I mean is from the original function f(x) = 2x + 3 how do you know that the 3 is a vertical shift and not horizontal shift?
$\text{Given$f(x)$a vertical (+ = up) shift of$c$is$f(x)+c$. A horizontal (+ = right) shift of$c$is$f(x-c)$. You can work these out for yourself}$

This of course assumes the x-axis is horizontal and positive to the right, and that the y-axis is vertical and positive upwards.

7. ## Re: transforming linear function

ok thank you.