UNIT OVERVIEW

Functions describe how quantities change and relate to each other. In Grade 10, you explored the basic shapes of parabolas, hyperbolas, and exponential graphs. Now you will learn how the parameter $p$ shifts these graphs horizontally, how to find the gradient at any point on a curve, and how to work with trigonometric functions.

By the end of this unit, you will be able to:

• Sketch and interpret graphs of $y = a(x + p)^2 + q$, understanding horizontal shifts
• Analyse and draw $y = \frac{a}{x + p} + q$ with its shifted asymptotes
• Work with $y = ab^{x + p} + q$ and exponential transformations
• Calculate the average gradient between two points on any curve
• Develop an intuitive understanding of the gradient at a point
• Plot and analyse $y = \sin\theta$, $y = \cos\theta$, and $y = \tan\theta$
• Investigate how parameters affect amplitude, period, and phase shift

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