Functions and Graphs
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A roller coaster engineer uses a polynomial function h(x)h(x)h(x) to model the height, in decametres, of a section of track relative to a horizontal distance xxx.

The function h(x)h(x)h(x) is defined for all x∈Rx \in \mathbb{R}x∈R. The profile of the track has the following features:

  • It touches the horizontal axis at a local minimum turning point at (2,0)(2, 0)(2,0).
  • It has a local maximum turning point at (−2,8)(-2, 8)(−2,8).
  • It crosses the vertical axis at the point (0,4)(0, 4)(0,4).
  • The graph behaves like a positive cubic, falling to the left and rising to the right.

On separate diagrams, sketch the curve with the following transformed equations:

i.

y=0.5h(x+2)y = 0.5h(x + 2)y=0.5h(x+2)

On each sketch, show clearly the coordinates of:

  • the point where the curve crosses the yyy-axis
  • any maximum or minimum turning points
[4]
ii.

y=h(2x)−5y = h(2x) - 5y=h(2x)−5

On each sketch, show clearly the coordinates of:

  • the point where the curve crosses the yyy-axis
  • any maximum or minimum turning points
[4]

Functions and Graphs Questions

Practise Edexcel A Level Maths Functions and Graphs with exam-style questions for A Level Maths. 100 questions covering 2.1 The Modulus Function, 2.2 Functions and Mappings, 2.3 Composite Functions, 2.4 Inverse Functions, 2.5 y=|f(x)| and y=f(|x|), 2.6 Combining Transformations, and 2.7 Solving Modulus Problems, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

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Functions and Graphs Questions

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