Anonymous functions in MATLAB - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of an anonymous function with vector input

What is the output of the following MATLAB code?

MATLAB

f = @(x) x.^2 + 2*x + 1;
result = f([1 2 3]);
disp(result);

A [4 9 16]

B [4 8 12]

C [4 9 15]

D [1 4 9]

💡 Hint

Remember that the operator .^ applies element-wise power to each element in the vector.

The anonymous function computes (x^2 + 2*x + 1) element-wise. For x=1: 1+2+1=4, for x=2: 4+4+1=9, for x=3: 9+6+1=16.

❓ Predict Output

intermediate

Output of nested anonymous functions

What is the output of this MATLAB code?

MATLAB

g = @(x) x + 1;
h = @(f, x) f(x) * 2;
result = h(g, 3);
disp(result);

A 6

B 7

C 8

D 9

💡 Hint

Evaluate the inner function g(3) first, then multiply by 2.

g(3) = 3 + 1 = 4. Then h calls g(3) and multiplies by 2, so 4 * 2 = 8.

🔧 Debug

advanced

Identify the error in anonymous function definition

Which option will cause an error when defining the anonymous function in MATLAB?

A f = @(x) x^2 + 3*x + 2;

B f = @(x) x.^2 + 3*x + 2;

C f = @(x) (x^2) + 3*x + 2;

D f = @(x) x**2 + 3*x + 2;

💡 Hint

Check the operator used for power in MATLAB.

MATLAB uses ^ for power, not **. Using ** causes a syntax error.

❓ Predict Output

advanced

Output of anonymous function with conditional expression

What is the output of this MATLAB code?

MATLAB

f = @(x) (x > 0) .* x + (x <= 0) .* 0;
result = f([-2 0 3]);
disp(result);

A [0 0 3]

B [-2 0 3]

C [0 0 0]

D [1 0 3]

💡 Hint

The function returns x if x is positive, otherwise 0.

For each element: if x>0, output x; else output 0. So -2 -> 0, 0 -> 0, 3 -> 3.

🧠 Conceptual

expert

Behavior of anonymous functions capturing variables

Consider the following MATLAB code. What is the value of y after running it?

MATLAB

a = 5;
f = @(x) x + a;
a = 10;
y = f(3);

A 8

B 13

C 3

D Error due to variable scope

💡 Hint

Anonymous functions use the current value of workspace variables at the time of execution.

The anonymous function looks up 'a' from the workspace when it is called. By then 'a' is 10, so f(3) = 3 + 10 = 13.

Practice

1. What is an anonymous function in MATLAB?

easy

A. A quick, unnamed function created using the '@' symbol.

B. A function saved in a separate file with a name.

C. A function that can only be used inside loops.

D. A function that requires no input arguments.

Solution

1. Step 1: Understand the definition of anonymous functions

   Anonymous functions in MATLAB are small, unnamed functions created using the '@' symbol.

2. Step 2: Compare options with the definition

   A quick, unnamed function created using the '@' symbol. correctly describes anonymous functions as quick, unnamed functions created with '@'. Other options describe named functions or incorrect properties.

3. Final Answer:

   A quick, unnamed function created using the '@' symbol. -> Option A

4. Quick Check:

   Anonymous function = unnamed function with '@' [OK]

Hint: Look for '@' symbol to identify anonymous functions [OK]

Common Mistakes:

• Confusing anonymous functions with regular named functions
• Thinking anonymous functions must have no inputs
• Assuming anonymous functions are saved in separate files

2. Which of the following is the correct syntax to create an anonymous function that squares its input x?

easy

A. f = @(x) x^2;

B. f = function(x) x^2;

C. f = @x x^2;

D. f = (x) => x^2;

Solution

1. Step 1: Recall MATLAB anonymous function syntax

   The correct syntax uses '@(args) expression;' so for squaring x, it is '@(x) x^2;'.

2. Step 2: Check each option

   f = @(x) x^2; matches the correct syntax. f = function(x) x^2; uses incorrect keyword 'function'. f = @x x^2; misses parentheses. f = (x) => x^2; uses arrow syntax from other languages.

3. Final Answer:

   f = @(x) x^2; -> Option A

4. Quick Check:

   Anonymous function syntax = @(args) expression [OK]

Hint: Remember '@(x) expression;' for anonymous functions [OK]

Common Mistakes:

• Omitting parentheses around input arguments
• Using 'function' keyword inside anonymous function
• Using arrow syntax from other languages

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

f = @(x) x + 5;
result = f(10);
disp(result);

medium

A. 5

B. 10

C. 15

D. Error

Solution

1. Step 1: Understand the anonymous function definition

   The function f adds 5 to its input x.

2. Step 2: Calculate the function output for input 10

   f(10) = 10 + 5 = 15.

3. Final Answer:

   15 -> Option C

4. Quick Check:

   10 + 5 = 15 [OK]

Hint: Apply input to expression inside @(x) function [OK]

Common Mistakes:

• Confusing input and output values
• Expecting function to multiply instead of add
• Thinking anonymous functions cause errors without file

4. Identify the error in this MATLAB anonymous function:

g = @x x^2 + 3;

medium

A. Anonymous functions cannot use addition.

B. Missing parentheses around input argument x.

C. The '@' symbol is not allowed here.

D. The function must be saved in a separate file.

Solution

1. Step 1: Check anonymous function syntax

   Anonymous functions require parentheses around input arguments, like '@(x)'.

2. Step 2: Identify the syntax error

   The code uses '@x' without parentheses, which is invalid syntax.

3. Final Answer:

   Missing parentheses around input argument x. -> Option B

4. Quick Check:

   Anonymous function input must be in parentheses [OK]

Hint: Always use @(input) with parentheses [OK]

Common Mistakes:

• Omitting parentheses around inputs
• Thinking '@' can be used without parentheses
• Believing anonymous functions need separate files

5. You want to create an anonymous function h that takes two inputs x and y and returns x squared plus y cubed. Which is the correct way to write this?

hard

A. h = @(x y) x^2 + y^3;

B. h = @(x,y) x^2 * y^3;

C. h = @(x,y) (x^2), (y^3);

D. h = @(x,y) x^2 + y^3;

Solution

1. Step 1: Understand multiple inputs in anonymous functions

   Multiple inputs are separated by commas inside parentheses: @(x,y).

2. Step 2: Check the expression for correct operations

   The function should return x squared plus y cubed, so use '+' operator, not '*'.

3. Final Answer:

   h = @(x,y) x^2 + y^3; -> Option D

4. Quick Check:

   Multiple inputs use commas; '+' adds results [OK]

Hint: Separate inputs with commas and use correct operators [OK]

Common Mistakes:

• Omitting commas between inputs
• Using wrong operators like multiplication instead of addition
• Trying to separate expressions with commas outside parentheses