How to Solve Function Notation

How to Solve Function Notation

Learn what the definition of function is and how to write a function using function notation and how to avaluate a function.

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Step by step guide to solve Function Notation and Evaluation

  • Functions are mathematical operations that assign unique outputs to given inputs.
  • Function notation is the way a function is written. It is meant to be a precise way of giving information about the function without a rather lengthy written explanation.
  • The most popular function notation is \(f(x)\) which is read “\(f\) of \(x\)”. Any letter can be used to name a function. for example: \(g(x)\), \(h(x)\), etc.
  • To evaluate a function, plug in the input (the given value or expression) for the function’s variable (place holder, \(x\) ).

Function Notation – Example 1:

Evaluate. \(h(n)=n^2-2\)
Find \(h(4)\).

Solution:

Substitute \((4)\) for \(n\) and solve. \(h(n)=n^2-2→h(4)=(4)^2-2→h(4)=16-2→h(4)=14\)

Function Notation – Example 2:

Evaluate. \(w(x)=4x-1\)
Find \(w(2)\).

Solution:

Substitute \((2)\) for \(x\) and solve. Then: \(w(x)=4x-1→w(2)=4(2)-1→w(2)=8-1→w(2)=7\)

Function Notation – Example 3:

Evaluate. \(w(x)=3x+1\)
Find \(w(4)\).

Solution:

Substitute \(x\) with \(4\): Then: \(w(x)=3x+1→w(4)=3(4)+1→w(x)=12+1→w(x)=13\)

Function Notation – Example 4:

Evaluate. \(h(n)=n^2-10\)
Find \(h(-2)\).

Solution:

Substitute \(n\) with \(-2\): \(h(n)=n^2-10→h(-2)=(-2)^2-10→h(-2)=4-10→h(-2)=-6\)

Exercises for Solving Function Notation

Evaluate each function.

  1. \(\color{blue}{w(x) = 3x + 1, find \ w(4)}\)
  2. \(\color{blue}{h(n) = n^2 – 10, find \ h(5)}\)
  3. \(\color{blue}{h(x) = x^3 + 8, find \ h(–2)}\)
  4. \(\color{blue}{h(n) = – 2n^2 – 6n, find \ h(2)}\)
  5. \(\color{blue}{g(n) = 3n^2 + 2n, find \ g(2)}\)
  6. \(\color{blue}{g(n) = 10n – 3, find \ g(6)}\)

Download Function Notation Worksheet

  1. \(\color{blue}{13}\)
  2. \(\color{blue}{15}\)
  3. \(\color{blue}{0}\)
  4. \(\color{blue}{-20}\)
  5. \(\color{blue}{16}\)
  6. \(\color{blue}{57}\)

Related to "How to Solve Function Notation"

How to Multiply and Divide in Scientific Notation
How to Multiply and Divide in Scientific Notation
How to Add and Subtract  in Scientific Notations
How to Add and Subtract in Scientific Notations

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