Function handles in MATLAB - Step-by-Step Execution

Concept Flow - Function handles

Define function handle

↓

Store function reference

↓

Call function via handle

↓

Execute function code

↓

Return result

Create a function handle to refer to a function, then call it through the handle to run the function and get results.

Execution Sample

MATLAB

f = @(x) x^2;
result = f(3);

Defines a function handle f that squares input x, then calls f with 3 to get 9.

Execution Table

Step	Action	Evaluation	Result
1	Define function handle f = @(x) x^2	f is a handle to anonymous function	f stores reference to function
2	Call f(3)	Compute 3^2	9 assigned to result
3	End	No more code	Execution stops

💡 No more statements to execute, program ends

Variable Tracker

Variable	Start	After Step 1	After Step 2	Final
f	undefined	function handle @(x) x^2	function handle @(x) x^2	function handle @(x) x^2
result	undefined	undefined	9	9

Key Moments - 2 Insights

Why do we use '@' when defining a function handle?

The '@' symbol tells MATLAB to create a function handle, not call the function immediately. See execution_table step 1 where f is assigned the handle.

What happens when we call f(3)?

Calling f(3) runs the function code with x=3, computing 3^2=9, as shown in execution_table step 2.

Visual Quiz - 3 Questions

Look at the execution table, what is stored in variable 'f' after step 1?

A The number 3

B The result 9

C A function handle to square a number

D Undefined

💡 Hint

Check variable_tracker row for 'f' after step 1

At which step is the function actually executed?

A Step 1

B Step 2

C Step 3

D Never

💡 Hint

Look at execution_table action 'Call f(3)'

If we change the input to f(4), what would be the new result in 'result' variable?

A 16

B 7

C 8

D 4

💡 Hint

Recall the function squares the input, see execution_table step 2

Concept Snapshot

Function handles in MATLAB:
- Use '@' to create a handle: f = @(x) expression;
- The handle stores a reference to the function code
- Call the function via handle: result = f(value);
- The function executes when called, returning output
- Useful for passing functions as arguments or storing them

Full Transcript

In MATLAB, a function handle is created using the '@' symbol followed by the function input and expression. This handle stores a reference to the function without running it immediately. When you call the handle with an input, MATLAB executes the function code and returns the result. For example, f = @(x) x^2 creates a function handle that squares its input. Calling f(3) runs the function with x=3 and returns 9. Variables change as the handle is created and then when the function is called. This lets you use functions flexibly in your code.

Practice

1. What does a function handle in MATLAB allow you to do?

easy

A. Store a reference to a function that can be called later

B. Create a new variable type

C. Automatically run a function without calling it

D. Convert a function into a string

Solution

1. Step 1: Understand what a function handle is

   A function handle is a way to refer to a function without executing it immediately.

2. Step 2: Identify the purpose of function handles

   They let you store and pass functions as variables to call later.

3. Final Answer:

   Store a reference to a function that can be called later -> Option A

4. Quick Check:

   Function handle = reference to function [OK]

Hint: Think of function handles as pointers to functions [OK]

Common Mistakes:

• Confusing function handles with function execution
• Thinking function handles create new data types
• Assuming function handles convert functions to strings

2. Which of the following is the correct way to create a function handle for the built-in function sin in MATLAB?

easy

A. handle = sin();

B. handle = &sin;

C. handle = @sin;

D. handle = sin;

Solution

1. Step 1: Recall the syntax for creating function handles

   In MATLAB, function handles are created using the @ symbol followed by the function name without parentheses.

2. Step 2: Check each option

   handle = @sin; uses @sin which is correct. handle = sin(); calls sin immediately, C uses & which is not MATLAB syntax, and D assigns the function name as a variable without @ which is invalid.

3. Final Answer:

   handle = @sin; -> Option C

4. Quick Check:

   Use @ before function name to create handle [OK]

Hint: Use @ before function name, no parentheses [OK]

Common Mistakes:

• Adding parentheses when creating handles
• Using & instead of @
• Assigning function name without @

3. What is the output of the following MATLAB code?

f = @(x) x^2 + 3;
result = f(2);

medium

A. 5

B. Error

C. 10

D. 7

Solution

1. Step 1: Understand the anonymous function definition

   The function f takes input x and returns x squared plus 3.

2. Step 2: Calculate the function output for x = 2

   f(2) = 2^2 + 3 = 4 + 3 = 7.

3. Final Answer:

   7 -> Option D

4. Quick Check:

   2 squared plus 3 equals 7 [OK]

Hint: Plug input into function formula carefully [OK]

Common Mistakes:

• Forgetting to square the input
• Adding instead of multiplying
• Expecting syntax error from anonymous function

4. Identify the error in the following MATLAB code that tries to create a function handle:

g = @(x) x + 1;
h = @g(2);

medium

A. Cannot use parentheses when creating a function handle

B. Function handle syntax is correct

C. Missing semicolon after function handle

D. Function handle must be created with a string

Solution

1. Step 1: Analyze the function handle creation

   The first line correctly creates an anonymous function g. The second line tries to create a handle h using @g(2), which is incorrect syntax.

2. Step 2: Understand correct function handle usage

   The @ operator must be followed by a function name or anonymous function without parentheses. Using parentheses calls the function, which is not allowed when creating a handle.

3. Final Answer:

   Cannot use parentheses when creating a function handle -> Option A

4. Quick Check:

   No parentheses allowed after @ when creating handles [OK]

Hint: No parentheses after @ when defining handles [OK]

Common Mistakes:

• Using parentheses after @
• Confusing function call with handle creation
• Thinking semicolon is required for correctness

5. You want to create a function handle that takes two inputs and returns their product plus 5. Which of the following anonymous function definitions is correct?

hard

A. f = @(x y) x * y + 5;

B. f = @(x, y) x * y + 5;

C. f = @(x, y) (x + y) * 5;

D. f = @(x, y) x * y + 5()

Solution

1. Step 1: Check the syntax for anonymous functions with multiple inputs

   Inputs must be separated by commas inside parentheses after @.

2. Step 2: Verify the expression matches the requirement

   f = @(x, y) x * y + 5; multiplies x and y, then adds 5, which matches the problem. f = @(x y) x * y + 5; misses the comma, C changes the operation, and D has invalid syntax with 5().

3. Final Answer:

   f = @(x, y) x * y + 5; -> Option B

4. Quick Check:

   Use commas between inputs and correct expression [OK]

Hint: Separate inputs with commas and write correct formula [OK]

Common Mistakes:

• Omitting commas between inputs
• Changing the math operation accidentally
• Adding parentheses after constants