Math 1 · Unit 7 · Lesson 2 · part 3 of 6
From the equation to a table to the curve
Building a table from the equation is easy once you know the two jobs.
From the equation to a table to the curve
Building a table from the equation is easy once you know the two jobs. Start at x = 0 with a, then multiply by b for each step to the right.
y = 3 · 2x
| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| y | 3 | 6 | 12 | 24 | 48 |
a = 3: start at 3. b = 2: double each step. The ratio down the table is 2.
Function notation, from Unit 2
f(x) = 3 · 2x. Then f(0) = 3 · 20 = 3 · 1 = 3, and f(4) = 3 · 24 = 3 · 16 = 48.
Watch the order. Do the power first, then multiply by a. 3 · 24 is 3 · 16 = 48, not 64. The exponent belongs to the base only.
y = 5 · 3x
f(0) = 5. f(1) = 15. f(2) = 5 · 9 = 45. f(3) = 5 · 27 = 135.
a = 5 is the y-intercept; b = 3 triples each step.
The two jobs, said out loud. a is the starting value, the y-intercept, because b to the zero is 1 and a times 1 is a. b is the growth factor, what you multiply by each step.