11th grade math dr adams notes

Here’s a compact set of starter notes for typical 11th grade math (Algebra 2 /
Precalculus level). You can copy this into a page and expand each section as you
learn.

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### 1. Functions and Graphs

**Function basics**

- A *function* maps each input (x) to exactly one output (f(x)).
- Domain: all allowed (x) values.
- Range: all possible (f(x)) values.
- Function notation: (y = f(x)).

**Transformations of functions**

If (y = f(x)):

- Vertical shift: (y = f(x) + k)
- (k > 0): shift up
- (k < 0): shift down
- Horizontal shift: (y = f(x - h))
- (h > 0): shift right
- (h < 0): shift left
- Reflections:
- (y = -f(x)): reflect over x-axis
- (y = f(-x)): reflect over y-axis
- Stretches/compressions:
- (y = a f(x)): vertical stretch if (|a| > 1), compression if (0 < |a| < 1)

**Inverse functions**

- (f^{-1}(x)) undoes (f(x)).
- To find:
1. Replace (f(x)) with (y)
2. Swap (x) and (y)
3. Solve for (y)
4. Rename (y) as (f^{-1}(x))
- Graph of inverse is reflection across the line (y = x).

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### 2. Quadratic Functions

**Standard forms**

- Standard form: (y = ax^2 + bx + c)
- Vertex form: (y = a(x - h)^2 + k)
- Vertex: ((h, k))
- Factored form: (y = a(x - r_1)(x - r_2))
- Zeros (x-intercepts): (x = r_1, r_2)

**Vertex and axis of symmetry**

- Vertex from standard form:
- (x = -dfrac{b}{2a}), then plug in to find (y)
- Axis of symmetry: vertical line (x = -dfrac{b}{2a})