Function Graphs: Solving Questions with Step-by-Step Guide

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SUMMARY

The discussion focuses on solving function graphing questions, particularly for GCSE mathematics. Key tasks include finding f(3) by locating the intersection on the graph, determining f(x)=6 by drawing a horizontal line at y=6 to find intersections, and calculating ff(1) by first finding f(1) and then evaluating f at that result. The participants confirm the correct approach to these problems, emphasizing the importance of visualizing intersections on the graph.

PREREQUISITES
  • Understanding of function notation and graphing
  • Familiarity with Cartesian coordinates
  • Basic knowledge of intersection points on graphs
  • Ability to interpret graphical data
NEXT STEPS
  • Study function evaluation techniques in graphing
  • Learn about horizontal and vertical line tests for functions
  • Explore composite functions and their graphical representations
  • Practice solving function-related problems using graphing tools
USEFUL FOR

Students preparing for GCSE mathematics, educators teaching graphing concepts, and anyone looking to strengthen their understanding of function evaluation and graphical interpretation.

tigerd12
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Hey all

Recently in a paper I was doing I came across a question which involved the graphing of a function. Now I am doing GCSE mathematics (the real exam) soon, having finished the syllabus; and have never come across anything like this before!

Here's the question

The graph y=f(x) is drawn

Find f(3)

Attempt: Do I go 3 along the X axis then go up see where it cuts the graph, draw a line there and find solutions?

Find f(x)=6

Attempt: Do I draw the line y=6 and see where this intersects with the graph? giving solutions

Find ff(1)?

Attempt: Do I.. do f(1), meaning go 1 across on the X axis, find the solution where it cuts the graph and go across to see the Y value, then after I obtain this value go along the X axis and find the point of intersection?

Thanks for any help, I really don't understand! I have never seen this type of question before
 
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f(3): your thinking is correct.

f(x)=6: correct, then you "look down" to the x axis.

ff(1): I guess that means f(f(1)). After you find y = f(1), go across the X axis to find y on the X axis, then find f(y).
 

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