Examples and practice
Graph transformations
Back to lessonPractice section 1 · Questions 1–6
Move the parabola horizontally · Move a reciprocal asymptote to the right · +4 more
Practice section 2 · Questions 7–12
Halve horizontal distances · Scale output distances about the x-axis · +4 more
Practice section 3 · Questions 13–18
Reflect input coordinates in the y-axis · Reflect a rational graph in the y-axis · +4 more
Practice section 4 · Questions 19–24
Complete the square before choosing transformations · Transform a cubic and find its exact intercepts · +4 more
Practice section 5 · Questions 25–30
Fold a rational graph above the x-axis · Sketch the modulus of a shifted straight line · +4 more
Practice section 6 · Questions 31–36
Compare curves with their reciprocals · Reciprocate three supplied sketches · +4 more
Practice section 7 · Questions 37–42
Start from the actual given graph f(x)+3 · Transform symbolic coordinates without choosing k · +4 more
- Start from the actual given graph f(x)+3
- Transform symbolic coordinates without choosing k
- Reverse a horizontal stretch, reflection and translation
- Sketch an exact rational function and two different modulus graphs
- Use zeros, poles and turning values to sketch three reciprocals
- Use partial fractions before sketching an absolute reciprocal
Practice section 8 · Questions 43–48
Recover f from a transformed input graph before reciprocating · Transform a piecewise curve and crop to the requested interval · +4 more
- Recover f from a transformed input graph before reciprocating
- Transform a piecewise curve and crop to the requested interval
- Transform the given graph f(2x) without doubling a scale factor
- Map labelled points and preserve reciprocal domains
- Reflect a two-branch graph and handle a reciprocal hole
- Apply successive transformations in their stated order
Practice section 9 · Questions 49–53
Compare modulus, negative scaling and reciprocal graphs · Undo a three-step transformation of an implicit curve · +3 more