Pre-Calculus - Applying more than one transformation to a function

[BlooCowz]

THANK YOU SO MUCH. Finally there's a video that doesn't show just one transformation at a time.

[knightofthebroho]

This video is actually wrong in its transformation of 2h(5-x). The horizontal shift should actually take place before the reflection. Inside he parentheses everything, including the order of transformations is reversed. Outside the parentheses things work normally and he order of transformations follows the order of operations.

Also, if you are given h(x)=af(bx+h)+k then the point (x, y) on f(x) will transform to the point ((x-h)/b, ay+k) on the graph of h(x). This rule works for any a, b, h, k except b=0, in which case h(x) is a constant function that just makes a horizontal line.

[ams]

The first problem at 1 minute is worked incorrectly. You need to factor the interior to correctly identify the reflection and horizontal transformation. So f(x)=2h(-1(x-5)) produces a vertical stretch by 2, a reflection over y-axis and shift right 5.

[frankjastrzembski]

The first problem that was finished at 5:40 does have the mistake pointed out in the comments that the shift should be to the right because 2h(5 -x) = 2h[-(x-5)]. It is tricky when the input (x) is effected by shifts, stretches and reflections to know the correct order to make these transformations. I leave it to the reader to start with a well understood function like y = x^3 and discover the correct order.

I comment only to say the original red graph of h(x) has all the info we need to check or find the correct graph of 2h(5-x). h has domain [-6, 1] So for our new function 2h(5-x), we know the input 5-x must be between -6 and 1. So, -6 5 - x 1 which leads to 4 x 11 as the domain of 2h(5-x). Plugging in 4 we have 2h(5 - 4) = 2h(1) = 2(0) = 0 so the new function contains the point (4, 0). Continue by plugging in 5, 6, 7, 8, 9, 10, 11 to arrive at the new graph.

[barrydavis]

The first time I check out one of your videos, you have a major conceptual mistake on a key topic.

[Master-epbe]

BLESS YOUR SOUL SIR ! GREETINGS FROM CANADA.. you deserve an actual award sir.

[midwestmatcha]

You literally save my life, thanks a lot

[ike]

perfectly explained. But i wish u could have squeezed a absolute value problem in there.