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Original practice · Free Online RevisionSkill · domain and range
State the domain and range of f(x)=1/(x−4)+2.
Functions & GraphsAdvancedMaths revision
Functions and Graphs (Advanced)
Analyse domains, ranges, asymptotes, inverses and composite behaviour across common function families.
Focus points
✓Analyse rational and piecewise functions.
✓Use inverses and compositions.
✓Reason from asymptotes and transformations.
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The Wise Owl
Guides study flow, revision planning, and calmer focus sessions.
Practice setQuestion lineup
Try each question first, reveal a hint when you need one, then check the worked answer. Mark them done as you go — finish the set to claim your chips.
8 revision questions
Question 2FluencyCore
Original practice · Free Online RevisionSkill · rational asymptotes
Find the vertical and horizontal asymptotes of y=(3x+1)/(x−2).
Question 3FluencyCore
Original practice · Free Online RevisionSkill · inverse rational function
Find the inverse of f(x)=(2x−1)/(x+3).
Question 4FluencyCore
Original practice · Free Online RevisionSkill · absolute-value graph
For f(x)=|x−2|+1, state the range.
Question 5ReasoningCore
Original practice · Free Online RevisionSkill · symmetry
Show that f(x)=f(6−x) for every x if f(t)=t²−6t+5. Explain the symmetry.
Question 6FluencyCore
Original practice · Free Online RevisionSkill · piecewise function
A function is defined by f(x)=x+2 for x<1 and f(x)=x² for x≥1. Find f(0), f(1), f(−3).
Question 7ChallengeStretch
Original practice · Free Online RevisionSkill · fixed points
Find all fixed points of f(x)=6/x, where a fixed point satisfies f(x)=x.
Question 8ChallengeStretch
Original practice · Free Online RevisionSkill · restricted range
Find the range of f(x)=x²−4x+7 for x≥3.