Questions: Functions and graph transformations
Pick a question type. Each time you get new numbers. Free ones are marked free.
Function notation
- Evaluate f(x) at a positive and a negative numberWork out, 3 marks, free, Higher tier
- Evaluate a quadratic function at a negative numberWork out, 2 marks, free, Higher tier
- Solve f(x) = kSolve, 2 marks, free, Higher tier
- f(a + 1) as an expressionFind, 2 marks, free, Higher tier
- f(x + k) for a quadraticExpand, 3 marks, free, Higher tier
- A function given in wordsWrite, 4 marks, free, Higher tier
- Solve f(x) = k for a quadratic fSolve, 2 marks, free, Higher tier
- A function in context: fares and chargesWork out, 3 marks, free, Higher tier
Composite and inverse functions
- Values of fg(x) and gf(x)Work out, 4 marks, free, Higher tier
- fg(x) or gf(x) as an expressionFind, 2 marks, free, Higher tier
- fg(x) when f is quadraticFind, 3 marks, free, Higher tier
- The inverse of a linear functionFind, 2 marks, free, Higher tier
- The inverse of (ax + b)/cFind, 3 marks, free, Higher tier
- A value of the inverse functionWork out, 2 marks, free, Higher tier
- Solve fg(x) = kSolve, 3 marks, free, Higher tier
- The inverse of a/(x + b)Find, 3 marks, free, Higher tier
Recognising graphs
- Match an equation to its sketchChoose, 1 mark, Plus, Higher tier
- Name the type of graphChoose, 1 mark, Plus, Higher tier
- Which equation matches the sketch?Choose, 1 mark, Plus, Higher tier
- Table of values for a cubic graphComplete, 2 marks, Plus, Higher tier
- Table of values for a reciprocal graphComplete, 2 marks, Plus, Higher tier
- Plot a cubic graphPlot, 2 marks, Plus, Higher tier
- Values on an exponential graphWork out, 3 marks, Plus, Higher tier
- Find a and b in y = abˣFind, 4 marks, Plus, Higher tier
- Read roots and the y-intercept from a cubic graphUse, 3 marks, Plus, Higher tier
Translating graphs
- Image of a point under y = f(x) + aWrite down, 2 marks, Plus, Higher tier
- Image of a point under y = f(x + a)Write down, 2 marks, Plus, Higher tier
- Turning point after a combined translationWrite down, 2 marks, Plus, Higher tier
- The vector of a translationWrite down, 2 marks, Plus, Higher tier
- Which equation is the translated graph?Choose, 1 mark, Plus, Higher tier
- Equation after a vertical translationWrite down, 2 marks, Plus, Higher tier
- Equation after a horizontal translationFind, 3 marks, Plus, Higher tier
- Complete the square, then give the translationFind, 4 marks, Plus, Higher tier
- Roots of f(x + a) = 0Solve, 2 marks, Plus, Higher tier
Reflections and trigonometric graphs
- Image of a point after a reflectionWrite down, 2 marks, Plus, Higher tier
- Which reflection maps f onto g?Choose, 1 mark, Plus, Higher tier
- Equation after a reflectionWrite down, 2 marks, Plus, Higher tier
- Turning point after a reflection and a translationWrite down, 2 marks, Plus, Higher tier
- Exact values of sin, cos and tanWrite down, 2 marks, Plus, Higher tier
- Solve sin x = k for 0 to 360 degreesSolve, 3 marks, Plus, Higher tier
- Solve cos x = k for 0 to 360 degreesSolve, 3 marks, Plus, Higher tier
- Period, maximum and key points of the trig graphsChoose, 1 mark, Plus, Higher tier
- Use the symmetry of the sine and cosine graphsWrite down, 2 marks, Plus, Higher tier
- Maximum or minimum point of a translated trig graphWrite down, 2 marks, Plus, Higher tier
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