Recognizing non-linear functions can be a little confusing at first, especially when you’re learning about graphs and functions in Year 8. But don’t worry! Once you understand the basics, it becomes much simpler.

Non-linear functions are different from linear functions, which create straight lines. Let’s go over some easy ways to identify non-linear functions.

1. Look at the Graph Shape

One of the easiest ways to spot non-linear functions is by looking at the shape of the graph.

Non-linear functions don’t make straight lines. Instead, they often look like curves or arches.

For example, quadratic functions like $y = x^2$ make a U-shaped graph called a parabola.

If you see a curve that bends, like a smile or a frown, you’re probably looking at a non-linear function.

2. Know the Different Types of Non-Linear Functions

There are several types of non-linear functions. Here are some important ones to remember:

• Quadratic Functions: These look like $y = ax^2 + bx + c$. They create a classic parabola.

• Cubic Functions: These have a degree of 3, like $y = ax^3 + bx^2 + cx + d$. They can bend one or two times.

• Exponential Functions: Like $y = a \cdot b^x$, these grow or decrease quickly. For example, $y = 2^x$ grows a lot as $x$ gets bigger.

• Trigonometric Functions: These look wavy, like sine and cosine graphs.

3. Check Tables of Values for Patterns

You can also find non-linear functions by looking at tables of values.

For example, if you calculate some values for $y = 2x^2$, your table might look like this:

| $x$ | $y$ | |-----|-----| | -2 | 8 | | -1 | 2 | | 0 | 0 | | 1 | 2 | | 2 | 8 |

Notice how as $x$ changes, the differences in $y$ are not the same.

For instance, when $x$ goes from 0 to 1, $y$ changes by 2. But when $x$ goes from 1 to 2, $y$ jumps by 6. This shows that the relationship between $x$ and $y$ isn’t linear.

4. Watch How Values Change

In linear functions, if you increase $x$ by 1, $y$ always changes the same amount.

In non-linear functions, this change can vary.

For example, if you look at how much $y$ changes as $x$ increases, you might notice different jumps. You could see a change of 1, then 3, and then maybe 7. This is a sign that you're looking at a non-linear function.

Conclusion

To sum it up, recognizing non-linear functions in Year 8 math is about looking at graph shapes, knowing the different types of functions, checking tables of values for changes, and observing how values shift.

Have fun exploring these functions. Happy graphing!