Transformation Of Graph Dse Exercise

Final: ( y = \frac1x+2 ) Step 2 (last applied): Horizontal shift left 3 → reverse: shift right 3. y = 1/( (x-3) + 2 ) = 1/(x - 1) Step 1 (first applied): Reflection in x-axis → reverse: reflect again in x-axis (multiply by -1). y = - 1/(x - 1) Therefore: ( h(x) = -\frac1x-1 ).

| Transformation | Effect on Graph | Algebraic Change | |----------------|----------------|-------------------| | | Shift right by (a) units ((a>0)) | (y = f(x - a)) | | | Shift left by (a) units | (y = f(x + a)) | | Translation (vertical) | Shift up by (b) units ((b>0)) | (y = f(x) + b) | | | Shift down by (b) units | (y = f(x) - b) | | Reflection (x-axis) | Flip vertically | (y = -f(x)) | | Reflection (y-axis) | Flip horizontally | (y = f(-x)) | | Stretch (vertical) | Multiply y-values by (k) ((k>1) stretch, (0<k<1) compress) | (y = k f(x)) | | Stretch (horizontal) | Divide x-values by (k) (i.e., (y = f(x/k))) – careful: stretch factor (1/k) | (y = f\left(\fracxk\right)) or (y = f(k' x))? Let’s clarify: | | Horizontal stretch factor (a) (from y-axis) | Points: ((x,y) \to (ax, y)) | (y = f(x/a)) | | Horizontal compression factor (a) | Points: ((x,y) \to (x/a, y)) | (y = f(ax)) | transformation of graph dse exercise