How to Solve Function Notation? (+FREE Worksheet!)
Learn what the definition of function is and how to write a function using function notation and how to evaluate a function.
Related Topics
- How to Add and Subtract Functions
- How to Multiply and Dividing Functions
- How to Solve Composition of Functions
- How to Find Inverse of a Function
Step by step guide to solve Function Notation
- 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, \(x\) ).
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Function Notation – Example 1:
Evaluate. \(h(n)=n^2-2\)
Find \(h(4)\).
Solution:
Substitute \((4)\) for \(n\) and solve. \(h(n)=n^2-2→h(4)=(4)^2-2→h(4)=16-2=14→h(4)=14\)
Function Notation – Example 2:
Evaluate. \(w(x)=4x-1\)
Find \(w(2)\).
Solution:
Substitute \((2)\) for \(x\) and solve. Then: \(w(x)=4x-1→w(2)=4(2)-1→w(2)=8-1=7→w(2)=7\)
Function Notation – Example 3:
Evaluate. \(w(x)=3x+1\)
Find \(w(4)\).
Solution:
Substitute \(x\) with \(4\): Then: \(w(x)=3x+1→w(4)=3(4)+1→w(4)=12+1=13→w(4)=13\)
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Function Notation – Example 4:
Evaluate. \(h(n)=n^2-10\)
Find \(h(-2)\).
Solution:
Substitute \(n\) with \(-2\): \(h(n)=n^2-10→h(-2)=(-2)^2-10→h(-2)=4-10=-6→h(-2)=-6\)
Exercises for Solving Function Notation
Evaluate each function.
- \(\color{blue}{w(x) = 3x + 1, find \ w(4)}\)
- \(\color{blue}{h(n) = n^2 – 10, find \ h(5)}\)
- \(\color{blue}{h(x) = x^3 + 8, find \ h(–2)}\)
- \(\color{blue}{h(n) =\space – 2n^2 – 6n, find \ h(2)}\)
- \(\color{blue}{g(n) = 3n^2 + 2n, find \ g(2)}\)
- \(\color{blue}{g(n) = 10n\space – 3, find \ g(6)}\)
Download Function Notation Worksheet
- \(\color{blue}{13}\)
- \(\color{blue}{15}\)
- \(\color{blue}{0}\)
- \(\color{blue}{-20}\)
- \(\color{blue}{16}\)
- \(\color{blue}{57}\)
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