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Lesson · Grade 10 · Foundations of Mathematics and Pre Calculus

Function notation: what f(3) means

  • Grade 10
  • Foundations of Mathematics and Pre Calculus
  • 2 min 10 s
  • British Columbia
  • BC10-MA-10

The video takes f(x) = 2x − 5 as a machine with an input and an output, and works out f(3) = 2(3) − 5 = 6 − 5 = 1, so the point (3, 1) is on the line y = 2x − 5. It then shows that f(3) does not mean f × 3 and works backwards from f(x) = 7 to x = 6, checks that f(6) = 7, marks (6, 7) on the graph, and ends with a one-line recap that f(3) is the output when the input is 3.

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In one sentence

The question this lesson answers

What does f of 3 mean? We will use one function the whole way: f of x equals 2x minus 5.

A function is a rule that takes each input and gives exactly one output.

Transcript

What the lesson says

What does f of 3 mean? We will use one function the whole way: f of x equals 2x minus 5.

A function is a rule that takes each input and gives exactly one output.

In f of x, f is the name of the function, and x stands for the input.

The rule 2x minus 5 says: multiply the input by 2, then subtract 5.

f of 3 means the output of f when the input is 3.

Replace x with 3: f of 3 equals 2 times 3, minus 5.

2 times 3 is 6, and 6 minus 5 is 1.

So f of 3 equals 1. The input 3 gives the output 1.

The graph of f shows each input with its output. It is the line y equals 2x minus 5.

So the point 3, 1 is on the graph: the input 3 is the x value, and the output 1 is the y value.

A common mistake is to read f of 3 as f times 3, but it does not mean that.

f is not a number: it is the name of the function, and the brackets hold the input.

Now work backwards: if f of x equals 7, what is x?

Replace f of x with its rule: 2x minus 5 equals 7.

Add 5 to both sides: 2x equals 12.

Divide both sides by 2: x equals 6.

Check: f of 6 is 2 times 6, minus 5. That is 12 minus 5, which is 7.

On the graph, go across from 7 to the line, then down to 6: the point 6, 7 is on it too.

Recap: f of 3 is the output of f when the input is 3. Here, f of 3 equals 1.

Curriculum

Where this fits

British Columbia, Grade 10

Foundations of Mathematics and Pre Calculus 10, Functions: functions and relations: connecting data, graphs, and situationsBC10-MA-10

Previous: Domain and Range from a Graph and a SituationNext: Telling the story of a graph

The outcomes and strands follow the British Columbia curriculum.

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