Transformation Of Graph Dse Exercise
Transformation of Graphs: A Comprehensive Exercise
- X-intercepts: Set $y = 0$. $x(x - 4) = 0 \implies x = 0 \text or x = 4$. Intercepts: $(0, 0)$ and $(4, 0)$.
- Vertex: For a parabola $y = ax^2 + bx + c$, the x-coordinate of the vertex is given by $x = -\fracb2a$. $x = -\frac-42(1) = 2$. Substitute $x=2$ back into equation: $y = (2)^2 - 4(2) = -4$. Vertex: $(2, -4)$.
Sample DSE‑style Questions
- The graph of y = 1/x is transformed to y = a/(x−2) + 3. Given the vertical and horizontal asymptotes, identify a and sketch for a = −2.
- A function f has zeros at x=−2,0,3. Describe the zeros after transformation g(x)=−2 f(0.5(x+4)) + 1.
- The curve y = ln x is shifted and stretched to y = 2 ln(3(x−1)) + 4. State domain and vertical asymptote.
- Identify the base function – Is it ( x^2, \sqrtx, \sin x, e^x ), or an abstract ( f(x) )?
- Deconstruct the given equation – Write it in the form ( a f(b(x - h)) + k ).
- Apply transformations in correct order (HS, VS, HT, VT inside-to-outside: ( b(x-h) ) first, then ( a ), then ( k )).
- Check key points – Vertices, intercepts, asymptotes, period/amplitude for trig.
- Verify with a test point – Substitute ( x=0 ) or a known value from original graph.
4. Combined Transformations (Order Matters!)
For ( y = a f(b(x - h)) + k ), the correct DSE order is: transformation of graph dse exercise
These transformations change the "tightness" or "steepness" of the graph. Vertical Change: , it is a vertical stretch. , it is a vertical compression. Horizontal Change: Transformation of Graphs: A Comprehensive Exercise
Order: Horizontal stretch/compress → Horizontal shift → Vertical stretch/compress → Reflection → Vertical shift. X-intercepts: Set $y = 0$
By mastering graph transformations, you will develop a deeper understanding of mathematical concepts and improve your problem-solving skills.