Non Linear Functions

Summary and Exam Tips for Non Linear Functions

Non Linear Functions is a subtopic of Algebra, which falls under the subject Mathematics in the IB MYP curriculum. Non-linear functions include a variety of graphs such as quadratic, trigonometric, cubic, and reciprocal graphs. These graphs are represented by equations like $y = x^2 - 4x + 3$ (a quadratic graph called a parabola), $y = \sin x$ (a trigonometric graph), $y = x^3 + 2x^2 - 4$ (a cubic graph), and $y = \frac{1}{x}$ (a reciprocal graph).

To find the gradient of a non-linear graph, one can use differentiation. This involves drawing a tangent to the curve, which is a straight line that touches the curve at only one point. The gradient of the curve at a point $(x, y)$ is equal to the gradient of the tangent at that point.

Exponential functions are defined as $f(x) = a^x$, where $a$ is a constant greater than 0. Examples include $f(x) = 2^x$ and $f(x) = \left(\frac{1}{2}\right)^x$. The domain of exponential functions is all real numbers $(-∞, ∞)$, while the range depends on the horizontal asymptote $y = d$.

Trigonometric functions like $f(x) = \sin \theta$ have a domain of angles in degrees or radians and a range of $[-1, 1]$.

Exam Tips

• Understand Graph Types: Familiarize yourself with different types of non-linear graphs such as quadratic, cubic, and trigonometric graphs. Recognize their equations and shapes.

• Practice Differentiation: Practice drawing tangents and using differentiation to find gradients of curves. This is crucial for solving problems related to non-linear graphs.

• Exponential Functions: Remember that the domain of exponential functions is all real numbers. Pay attention to the base $a$ to determine the range.

• Trigonometric Functions: Know the domain and range of basic trigonometric functions. Practice converting between degrees and radians.

• Use Graphing Software: Utilize graphing software to visualize and understand the behavior of non-linear functions. This can aid in better comprehension and retention.