To draw graphs from equations in Year 11 Maths easily, just follow these simple steps:

1. Know the Type of Function

First, figure out what kind of equation you have.

Is it linear (a straight line), quadratic (a U-shape), cubic (looks like a wave), exponential (growing fast), or trigonometric (like a wave)?

This helps you understand what the graph will look like.

2. Find Important Features

• Intercepts:
  • To find the $y$-intercept, set $x = 0$ and solve.
  • For $x$-intercepts, set $y = 0$ and solve for $x$.
• Symmetry: Check if the graph is symmetric. If it mirrors around the $y$-axis, it's even. If it has rotational symmetry (like turning it upside down), it’s odd.

3. Understand the Domain and Range

The domain is all the possible $x$ values, and the range is all the possible $y$ values.

For example, in the quadratic function $f(x) = x^2$, you can use any number for $x$ (all real numbers), but $y$ will always be $0$ or more.

4. Look at Behavior at Extremes

See what happens to the function when $x$ gets really big or really small (positive and negative infinity).

For example, if you have $f(x) = ax^2 + bx + c$ and $a$ is positive, your graph will curve upwards.

5. Plot Points

Pick some $x$ values, calculate the $y$ values that go with them, and plot those points on a graph.

6. Draw the Graph

Using the important features and the points you plotted, sketch the graph carefully. Make sure you get the curves and intercepts just right.

By following these steps, students can create accurate and helpful graphs from different equations!