Transformation Of Graph Dse Exercise File

Stationary points occur when ( g'(x)=0 ). ( g(x) = 2f(1-x) + 1 ) ( g'(x) = 2 \cdot f'(1-x) \cdot (-1) = -2 f'(1-x) ) Set ( g'(x)=0 \implies f'(1-x)=0 ).

Thus stationary points at ( x=0, 2 ). Trig graphs test horizontal scaling (period change) and vertical scaling (amplitude) most intensely. transformation of graph dse exercise

The graph of ( y = \cos x ) is transformed to ( y = 3\cos(2x - \pi) + 1 ). Describe the sequence. Stationary points occur when ( g'(x)=0 )

A and D are equivalent and correct. Reflection first: ( y = -\sin x ), then +2. Exercise Set 2: Finding the Original Graph (Reverse Transformation) DSE often asks: Given the image graph, find the pre-image function. Trig graphs test horizontal scaling (period change) and

Sketch ( y = |x^2 - 4| - 1 ). How many x-intercepts?

Now ( f'(x)=3x^2-3 = 3(x^2-1) ). So ( f'(1-x)=0 \implies (1-x)^2 - 1 =0 \implies (1-x)^2=1 ) ( \implies 1-x = \pm 1 \implies x=0 ) or ( x=2 ).