Question

Vocabulary words




Lesson 2
dilation




family of functions




horizontal compression




horizontal reflection




horizontal shift




horizontal stretch




parent function




reflection




slope




transformation




translation




vertical compression




vertical reflection




vertical shift




vertical stretch




Lesson 3-5 –no new vocabulary
Lesson 6
even function




odd function

Answer 1

Here are concise definitions and quick examples for each vocabulary word you listed.

Lesson 2

- Dilation
- A scaling of a graph that makes it wider or narrower (can be horizontal or vertical). Achieved by multiplying x or f(x) by a constant.
- Example: y = 2f(x) is a vertical dilation (stretch by factor 2).

- Family of functions
- A set of functions that share the same general shape or rule type (e.g., linear family, quadratic family).
- Example: all quadratics ax^2 + bx + c.

- Horizontal compression
- A narrowing of the graph in the x-direction. Replace x by bx with |b|>1.
- Example: y = f(2x) compresses horizontally by factor 1/2.

- Horizontal reflection
- A mirror image across the y-axis. Replace x by −x.
- Example: y = f(−x).

- Horizontal shift
- A left or right movement of the graph. Replace x by (x − h); h>0 shifts right, h<0 shifts left.
- Example: y = f(x − 3) shifts the graph 3 units right.

- Horizontal stretch
- A widening of the graph in the x-direction. Replace x by bx with 0<|b|<1.
- Example: y = f(0.5x) stretches horizontally by factor 2.

- Parent function
- The simplest function of a family, used as a base for transformations.
- Examples: f(x)=x (linear), f(x)=x^2 (quadratic), f(x)=|x| (absolute value).

- Reflection
- Flipping a graph across a line (x-axis or y-axis). y → −y gives reflection across the x-axis; x → −x gives reflection across the y-axis.
- Examples: y = −f(x) (x-axis reflection), y = f(−x) (y-axis reflection).

- Slope
- The steepness of a line: rise/run. For y = mx + b, slope = m.
- Example: slope 2 means up 2 for right 1.

- Transformation
- Any change to a graph (translation, reflection, dilation, or combination).
- Example: y = −2f(x − 1) + 3 is a combination of transformations.

- Translation
- Another word for shift: moving the graph without rotating or scaling.
- Example: y = f(x) + 4 translates up 4 units.

- Vertical compression
- A shrinking of the graph in the y-direction. Multiply the function by a with 0<|a|<1.
- Example: y = 0.5 f(x) compresses vertically by factor 1/2.

- Vertical reflection
- Reflection across the x-axis: y = −f(x).

- Vertical shift
- Moving the graph up or down by adding/subtracting outside the function.
- Example: y = f(x) + 2 moves up 2 units.

- Vertical stretch
- A stretching of the graph in the y-direction. Multiply the function by a with |a|>1.
- Example: y = 3 f(x) stretches vertically by factor 3.

Quick note on inside vs outside changes:
- Inside changes to x (f(x − h), f(bx)) produce horizontal shifts/stretches/compressions/reflections.
- Outside changes (af(x) + k, −f(x)) produce vertical stretches/compressions/reflections/shifts.

Lessons 3–5
- No new vocabulary (per your list).

Lesson 6

- Even function
- A function symmetric about the y-axis. f(−x) = f(x) for all x in the domain.
- Example: f(x)=x^2, f(x)=cos(x).

- Odd function
- A function symmetric about the origin. f(−x) = −f(x) for all x in the domain.
- Example: f(x)=x^3, f(x)=sin(x).

If you want, I can make flashcards, provide example graphs, or give short practice problems for any of these terms. Which would you like next?