1. **Graphs of Functions**: A function is a rule that assigns each input exactly one output. The graph of a function is the set of all points $(x, y)$ where $y = f(x)$. To graph a function, pick $x$ values, find corresponding $y$ values, then plot these points. 2. **Graphing Techniques - Transformations**: Transformations change a graph's shape or position. - **Translations** move the graph up, down, left, or right. For example, $y = f(x) + k$ moves the graph up by $k$ units. - **Reflections** flip the graph over an axis. $y = -f(x)$ reflects it over the x-axis. - **Stretching/Compressing** changes the size. $y = af(x)$ stretches vertically if $|a| > 1$, compresses if $0 < |a| < 1$. - Horizontal transformations affect the $x$ inside the function, like $y = f(x - h)$ shifts right by $h$. 3. **Angle Measure**: Angles are measured in degrees or radians. One full rotation is $360^\circ$ or $2\pi$ radians. To convert, use $$\text{radians} = \text{degrees} \times \frac{\pi}{180}$$ 4. **Right Triangle Trigonometry**: In right triangles, trigonometric ratios relate angles to side lengths. - **Sine**: $\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$ - **Cosine**: $\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$ - **Tangent**: $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$ To solve problems, identify the angle, the sides involved, and use appropriate ratio formulas. These foundational concepts will help in understanding grade 11 precalculus topics and prepare you well for your midterm.