Transformation Of Graph Dse Exercise -

A. Translate left 2, then reflect in (x)-axis B. Translate right 2, then reflect in (y)-axis C. Reflect in (x)-axis, then translate left 2 D. Reflect in (y)-axis, then translate right 2 Given ( y = f(x) ) passes through ( A(4, -1) ).

Translate ( y = x^2 ) right 2, up 1.

Find the coordinates of the image of (A) after the transformation ( y = 2f(x - 3) + 1 ). transformation of graph dse exercise

Vertex: ( (5, -1) )

Express ( f(x) ) in the form ( (x - h)^2 + k ). (b) Describe the transformation from ( y = x^2 ) to ( y = f(x) ). (c) The graph of ( y = f(x) ) is reflected in the (x)-axis, then translated 3 units right. Write the equation of the resulting graph. (d) Find the vertex of the final graph in (c). Answers 1.(a) i. ( y = f(x) + 3 ) ii. ( y = f(x + 2) ) iii. ( y = -f(x) ) iv. ( y = f(-x) ) v. ( y = 4f(x) ) vi. ( y = f(2x) ) Reflect in (x)-axis, then translate left 2 D

If the transformed graph passes through ( B(1, 5) ) under ( y = -f(x) + 3 ), find the original point on ( y = f(x) ) corresponding to (B). 4. Graph sketching Sketch ( y = \sqrt{x} ). On the same diagram, sketch ( y = \sqrt{x - 2} + 1 ) and ( y = -\sqrt{x} ). Label at least 2 points on each curve. 5. Real DSE-style (Long question) Let ( f(x) = x^2 - 4x + 5 ).

Original: ( y = (x - 2)^2 + 1 ) Reflect in (x)-axis: ( y = -(x - 2)^2 - 1 ) Translate right 3: ( y = -( (x - 3) - 2)^2 - 1 ) Simplify: ( y = -(x - 5)^2 - 1 ) Find the coordinates of the image of (A)

The questions cover translation, reflection, and scaling. 1. Basic transformations (Short Questions) (a) The graph of ( y = f(x) ) is given. Write the equation of the image after each transformation:

i. Translate 3 units upward. ii. Translate 2 units to the left. iii. Reflect across the (x)-axis. iv. Reflect across the (y)-axis. v. Enlarge vertically by a factor of 4. vi. Enlarge horizontally by a factor of ( \frac12 ). The graph of ( y = x^2 ) is transformed to ( y = 3(x - 1)^2 + 5 ). Describe the sequence of transformations in order. 2. Matching equations with transformations (Multiple Choice) Which of the following represents the graph of ( y = -f(x + 2) ) if ( y = f(x) ) is the original graph?