Mathematical expressions with LaTeX in Matplotlib - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of LaTeX formatted plot title

What will be the title text shown on the plot after running this code?

Matplotlib

import matplotlib.pyplot as plt
plt.plot([1, 2, 3], [1, 4, 9])
plt.title(r'$y = x^2$')
plt.show()

A The plot title shows the text: y = x^2 with superscript formatting

B The plot title shows the text: y = x2 without superscript

C The plot title is empty with no text shown

D The plot title shows the raw string: $y = x^2$ without formatting

💡 Hint

Look at how LaTeX math expressions are wrapped with $ signs inside the raw string.

Using r'$y = x^2$' in plt.title tells matplotlib to render the text as a LaTeX math expression, so the superscript 2 appears correctly.

❓ data_output

intermediate

Number of tick labels with LaTeX formatting

How many x-axis tick labels will be shown after running this code?

Matplotlib

import matplotlib.pyplot as plt
import numpy as np
x = np.linspace(0, 2, 5)
plt.plot(x, x**2)
plt.xticks(x, [f'$x_{{{int(i)}}}$' for i in x])
plt.show()

A 5 tick labels with LaTeX formatted subscripts x_0, x_0.5, x_1, x_1.5, x_2

B 5 tick labels with LaTeX formatted subscripts x_0, x_0, x_1, x_1, x_2

C 5 tick labels with LaTeX formatted subscripts x_0, x_1, x_2, x_3, x_4

D 5 tick labels with LaTeX formatted subscripts x_0, x_1, x_2, x_3, x_5

💡 Hint

Look carefully at how the labels are created using int(i) for each tick value.

The labels use int(i) which truncates decimals, so 0.5 and 1.5 become 0 and 1 respectively, causing repeated labels.

❓ visualization

advanced

Correct LaTeX rendering of integral expression in plot

Which option produces a plot with the title showing the integral \( \int_0^1 x^2 dx \) correctly formatted?

A plt.title(r'\int_0^1 x^2 dx')

B plt.title('$\int_0^1 x^2 dx$')

C plt.title('\int_0^1 x^2 dx')

D plt.title(r'$\int_0^1 x^2 dx$')

💡 Hint

Raw strings (r'') help avoid needing to double escape backslashes in LaTeX.

Option D uses a raw string with proper LaTeX math delimiters, so the integral renders correctly. Option D misses raw string so backslash escapes may fail. Options A and D miss math delimiters or have wrong escaping.

🔧 Debug

advanced

Identify the error in LaTeX expression for plot label

What error will this code produce when run?

Matplotlib

import matplotlib.pyplot as plt
plt.plot([1, 2, 3], [1, 4, 9])
plt.xlabel(r'$\frac{1}{2$')
plt.show()

A RuntimeError from matplotlib about invalid LaTeX syntax

B SyntaxError due to unmatched brace in LaTeX expression

C The label shows raw text $\frac{1}{2$ without formatting

D No error, label shows fraction 1/2 correctly

💡 Hint

Check if all braces in the LaTeX expression are properly closed.

The LaTeX expression has an opening brace '{' without a matching closing brace '}', causing matplotlib to raise a runtime error when rendering.

🚀 Application

expert

Create a plot with multiple LaTeX formatted annotations

Which code snippet correctly adds two LaTeX formatted annotations at points (1,1) and (2,4) on the plot?

A plt.annotate(r'y=1', (1,1)); plt.annotate(r'y=2^2', (2,4))

B plt.annotate('$y=1$', (1,1)); plt.annotate('$y=2^2$', (2,4))

C plt.annotate(r'$y=1$', (1,1)); plt.annotate(r'$y=2^2$', (2,4))

D plt.annotate('y=1', (1,1)); plt.annotate('y=2^2', (2,4))

💡 Hint

Raw strings with $ delimiters are needed for LaTeX math rendering in annotations.

Option C uses raw strings with $...$ which matplotlib interprets as LaTeX math, so annotations render correctly. Option C misses raw string so backslash escapes may fail. Options C and D miss $ delimiters so no math formatting.

Practice

1. What is the correct way to include a simple fraction \(\frac{1}{2}\) in a matplotlib title using LaTeX?

easy

A. plt.title(r"$\frac{1}{2}$")

B. plt.title("$\frac{1}{2}$")

C. plt.title("\frac{1}{2}")

D. plt.title(r"\frac{1}{2}")

Solution

1. Step 1: Use raw string for LaTeX in matplotlib

   Raw strings (prefix r) prevent Python from treating backslashes as escape characters.

2. Step 2: Wrap LaTeX math expression in dollar signs

   Dollar signs tell matplotlib to interpret the string as math text.

3. Final Answer:

   plt.title(r"$\frac{1}{2}$") -> Option A

4. Quick Check:

   Raw string + $...$ = Correct LaTeX [OK]

Hint: Always use raw strings and $...$ for LaTeX in matplotlib [OK]

Common Mistakes:

• Forgetting raw string causes errors
• Missing dollar signs disables math mode
• Using plain string with backslashes causes escape errors

2. Which of the following is the correct syntax to display the integral symbol \(\int\) in a matplotlib axis label?

easy

A. plt.xlabel(r"Integral \int")

B. plt.xlabel("\int")

C. plt.xlabel("$\int$")

D. plt.xlabel(r"$\int$ Integral")

Solution

1. Step 1: Use raw string with dollar signs for LaTeX math

   Raw string avoids escape issues; dollar signs enable math mode.

2. Step 2: Place integral symbol inside dollar signs

   Integral symbol \int must be inside $...$ to render properly.

3. Final Answer:

   plt.xlabel(r"$\int$ Integral") -> Option D

4. Quick Check:

   Raw string + $\int$ = Integral symbol shown [OK]

Hint: Put math symbols inside $...$ and use raw strings [OK]

Common Mistakes:

• Not using $...$ around math symbols
• Not using raw strings causing backslash errors
• Placing math symbols outside math mode

3. What will be the output of this code snippet?

import matplotlib.pyplot as plt
plt.title(r"$\sqrt{16} = 4$")
plt.show()

medium

A. Title shows raw text including backslashes and braces

B. Title shows the square root symbol with '16 = 4' correctly formatted

C. Title shows 'sqrt{16} = 4' without square root symbol

D. Code raises a syntax error due to backslashes

Solution

1. Step 1: Raw string with $...$ enables LaTeX math rendering

   The string r"$\sqrt{16} = 4$" renders the square root symbol with 16 inside.

2. Step 2: plt.title displays the formatted math expression as title

   The plot title will show the square root symbol and the equation correctly.

3. Final Answer:

   Title shows the square root symbol with '16 = 4' correctly formatted -> Option B

4. Quick Check:

   Raw string + $\sqrt{}$ = Rendered square root [OK]

Hint: Raw string + $\sqrt{}$ shows square root symbol [OK]

Common Mistakes:

• Not using raw string causes escape errors
• Missing $...$ disables math rendering
• Expecting plain text instead of formatted math

4. Identify the error in this matplotlib code that tries to display the Greek letter alpha \(\alpha\) in the legend:

plt.plot([1,2,3], label="$\alpha$")
plt.legend()
plt.show()

medium

A. Missing raw string prefix causing backslash escape error

B. Legend function is missing parentheses

C. Label string should not use dollar signs

D. Plot data is invalid

Solution

1. Step 1: Check string for LaTeX math in label

   Using "$\alpha$" without raw string causes Python to treat \a as escape sequence.

2. Step 2: Add raw string prefix to fix backslash escape

   Change label to r"$\alpha$" to correctly render Greek letter alpha.

3. Final Answer:

   Missing raw string prefix causing backslash escape error -> Option A

4. Quick Check:

   Use raw string for LaTeX labels [OK]

Hint: Always use raw strings for LaTeX in labels [OK]

Common Mistakes:

• Forgetting raw string prefix
• Removing dollar signs disables math mode
• Misunderstanding legend syntax

5. You want to label the y-axis with the formula for the quadratic roots:
\(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
Which matplotlib code correctly displays this formula using LaTeX?

hard

A. plt.ylabel(r"x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}")

B. plt.ylabel("$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$")

C. plt.ylabel(r"$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$")

D. plt.ylabel("x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}")

Solution

1. Step 1: Use raw string to avoid backslash escape errors

   The formula contains many backslashes, so raw string (r"...") is needed.

2. Step 2: Wrap the entire formula in dollar signs for math mode

   Dollar signs enable LaTeX math rendering in matplotlib labels.

3. Final Answer:

   plt.ylabel(r"$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$") -> Option C

4. Quick Check:

   Raw string + $...$ = Correct LaTeX formula [OK]

Hint: Use raw string and $...$ to display complex formulas [OK]

Common Mistakes:

• Not using raw string causes syntax errors
• Missing dollar signs disables math rendering
• Using plain strings with backslashes