Transformation Of Graph Dse Exercise ★ Premium

, it is a horizontal compression (the graph squishes toward the y-axis).

is translated 2 units to the left, then compressed vertically by a factor of 0.5, and finally reflected across the x-axis, find the equation of the new graph Translate left by 2: Compress vertically by 0.5: Reflect across x-axis: Result:

Usually, it is easier to deal with shifts and stretches involving before moving to transformation of graph dse exercise

Translation involves moving the entire graph without changing its shape or orientation. , the graph moves up , the graph moves down Horizontal Shift: , the graph moves right units (e.g., moves 3 units right). , the graph moves left units (e.g., moves 3 units left). 2. Reflection: Flipping the Graph Reflection creates a mirror image of the original function. Reflection across the x-axis: All y-values change signs. The top becomes the bottom. Reflection across the y-axis:

💡 Always check the wording carefully. "Reflected across the x-axis" is a vertical change, while "reflected across the y-axis" is a horizontal change. , it is a horizontal compression (the graph

Choose specific coordinates, such as the vertex or intercepts, and apply the transformations to those points one by one.

Draw the new graph and check if the changes match the algebraic operations (e.g., did a actually flip it upside down?). Sample DSE Exercise Problem: Let be a function. If the graph of , the graph moves left units (e

by 2 compresses it. Transformations outside the function (affecting ) behave intuitively. Step-by-Step Breakdown Recognize the original

Transformations happening inside the function brackets (affecting

) usually behave the opposite of what you might expect. For example, adding to moves the graph left, and multiplying