Transformation Of Graph Dse Exercise Site

The graph of ( y = 2^x ) is reflected in the line ( y = x ), then stretched vertically by factor 3, then translated 2 units down. Find the equation of the resulting curve. Answer: Reflection in ( y=x ) gives inverse: ( y = \log_2 x ). Then vertical stretch ×3: ( y = 3 \log_2 x ). Then down 2: ( y = 3 \log_2 x - 2 ).

The graph of ( y = f(x) ) is translated 3 units right and then reflected in the y-axis to become ( y = \sqrt4 - x^2 ). Find ( f(x) ). transformation of graph dse exercise

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 ). The graph of ( y = 2^x )

Start with ( y = x^2 - 4 ) (vertex at (0,-4), roots at ±2). Step 2: Apply modulus: ( y = |x^2 - 4| ) – reflect negative part above x-axis. Step 3: Subtract 1: shift graph down by 1. Then vertical stretch ×3: ( y = 3 \log_2 x )

Now go forth and transform every graph the DSE throws at you!

The graph of ( y = \cos x ) is transformed to ( y = 3\cos(2x - \pi) + 1 ). Describe the sequence.

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