Understanding Graphs in Algebra

Graphs visually represent mathematical relationships between variables. They help us understand the behavior of functions and equations.

What is a Graph?

A graph is a visual representation of the relationship between variables, usually on a coordinate plane.

Types of Graphs

• Line graphs: Show linear relationships.
• Parabolas: Show quadratic relationships.
• Other curves: Exponential, logarithmic, etc.

Plotting Points

Each point on a graph has coordinates \( (x, y) \).

To plot a function, calculate \( y \) for various \( x \) values and plot the points.

Interpreting Graphs

Graphs can show intercepts, slopes, maxima, minima, and asymptotes.

They help us solve equations and inequalities visually.

Practice Problems

1. Graph \( y = 2x + 1 \).
2. Find the x- and y-intercepts of \( y = x^2 - 4 \).
3. Sketch the graph of \( y = \frac{1}{x} \).