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Introduction to Functions and Graphs

Learn what a function is, like f(x)=2x+1f(x) = 2x + 1, and how to visualise it using tables and graphs. Let’s get started! 🚀

Introduction to Functions and Graphs - introduction visual

Video Lesson

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Flashcards

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Visual representation of function notation showing the function f(x) = 2x + 1 and its calculated outputs for f(1), f(2), and f(3).Steps to graph a function showing a table of values for f(x)=2x+1 and its corresponding plotted graph with points.2 graphs showing non-functions: one with a circle and another with a vertical line, explaining that one x-value must not have multiple y-values.Graph showing function values with examples: f(-2) = -3 and f(x) = 0 at x = -4, 0, 5, with a function definition.

🛎️ What Does Function Notation f(x) Mean?

  • f(x)f(x) shows the output when the input is xx.
  • To find f(3)f(3), substitute x=3x = 3 into the rule.
  • For example, if f(x)=2x+1f(x) = 2x + 1, then f(3)=2(3)+1=7f(3) = 2(3) + 1 = 7.

🛎️ How to Graph a Function?

  • First create a table by choosing x-values and finding the matching f(x) values.
  • Then plot the points on a graph and join them with a straight or smooth line.

🛎️ Does a Graph Represent a Function?

  • A graph is a function if each x-value has only one y-value.
  • If one x-value has more than one y-value, it is not a function.

🛎️ Reading Function Values from Graphs

  • To find f(x), go to the x-value and read the y-value on the graph.
  • Solving f(x) = 0 means the y-value is zero. This happens where the graph crosses the x-axis.

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Introduction to functions and graphs

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