Function transformations, sequences, and conic sections for a precalculus course, distinct from the calculus-specific decks.
37 cards · basic cards · AI-written, checked twice. Edit anything.
- How does f(x-h) transform the graph of f(x)?
- Horizontal shift right by h units
- How does f(x)+k transform the graph of f(x)?
- Vertical shift up by k units
- What happens to the graph of y = f(x) when you compute a*f(x) with a > 1?
- Vertical stretch by factor of a
- What happens to the graph of y = f(x) when you compute a*f(x) with 0 < a < 1?
- Vertical compression by factor of a
- What happens to the graph of y = f(x) when you compute f(b*x) with b > 1?
- Horizontal compression by factor of 1/b
- What happens to the graph of y = f(x) when you compute f(x/c) with c > 1?
- Horizontal stretch by factor of c
- How does -f(x) transform the graph of f(x)?
- Reflection across the x-axis
- What is an even function?
- A function where f(-x) = f(x) for all x in its domain
- What is an odd function?
- A function where f(-x) = -f(x) for all x in its domain
- When combining multiple transformations, does the order matter?
- Yes, the order affects the final result. Apply inside operations first, then outside operations.
- If f has domain [0, 4], what is the domain of f(x-2)?
- [2, 6]
- Define an arithmetic sequence.
- A sequence where consecutive terms have a constant difference
- What is the common difference in an arithmetic sequence?
- The constant difference d between consecutive terms, where a(n+1) - a(n) = d
- Write the formula for the nth term of an arithmetic sequence.
- a_n = a_1 + (n-1)d
- Write the formula for the sum of the first n terms of an arithmetic sequence.
- S_n = n/2 * (a_1 + a_n) or equivalently S_n = n/2 * (2a_1 + (n-1)d)