Comparing Linear, Exponential, and Quadratic Models
Unit 12: Polynomials, Modeling & Comparison · AI-F.LE.1, AI-F.IF.4, AI-F.IF.9
Algebra I Regents
Notes
Look at how it grows. A table 3, 6, 9, 12 is linear (+3). A table 3, 6, 12, 24 is exponential (×2). A table 3, 6, 11, 18 has first differences 3, 5, 7 (second differences 2) — quadratic.
Vocabulary
first difference: The change from one y-value to the next in a table with uniform x-steps.
Practice (no calculator unless marked)
Which function will have the greatest value when x > 1?
A. g(x) = 2(5)ˣ
B. f(x) = 2x + 5
C. h(x) = 2x² + 5
D. k(x) = 2x³ + 5
Which function will have the greatest value when x > 1?
A. g(x) = 2(5)ˣ
B. f(x) = 2x + 5
C. h(x) = 2x² + 5
D. k(x) = 2x³ + 5
Which function will have the greatest value when x > 1?
A. g(x) = 2(5)ˣ
B. f(x) = 2x + 5
C. h(x) = 2x² + 5
D. k(x) = 2x³ + 5
Which function will have the greatest value when x > 1?
A. g(x) = 2(5)ˣ
B. f(x) = 2x + 5
C. h(x) = 2x² + 5
D. k(x) = 2x³ + 5
Which function will have the greatest value when x > 1?
A. g(x) = 2(5)ˣ
B. f(x) = 2x + 5
C. h(x) = 2x² + 5
D. k(x) = 2x³ + 5
Which function will have the greatest value when x > 1?
A. g(x) = 2(5)ˣ
B. f(x) = 2x + 5
C. h(x) = 2x² + 5
D. k(x) = 2x³ + 5
Which function will have the greatest value when x > 1?
A. g(x) = 2(5)ˣ
B. f(x) = 2x + 5
C. h(x) = 2x² + 5
D. k(x) = 2x³ + 5
Which function will have the greatest value when x > 1?