COMPOSITION OF FUNCTIONS NYOS CHARTER SCHOOL PRECALCULUS BEFORE
COMPOSITION OF FUNCTIONS NYOS CHARTER SCHOOL PRECALCULUS
BEFORE I FORGET… • Pledge of Allegiance • Moment of Silence • Index Cards • Max/Min • Even/Odd/Neither
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COMBINING FUNCTIONS • Operations on Functions • (f + g)(x) = f(x) + g(x) • (f – g)(x) = f(x) – g(x) • (f * g)(x) = f(x) * g(x) • =
COMBINING FUNCTIONS Example: Let f(x) = 2 x 2 (f + g)(x) = f(x) + g(x) and g(x) = 5 x. Find (f + g)(x).
COMBINING FUNCTIONS Example: Let f(x) = 2 x 2 (f + g)(x) = f(x) + g(x) = 2 x 2 + 5 x and g(x) = 5 x. Find (f + g)(x).
COMBINING FUNCTIONS Example: Let f(x) = x 2 + 1 (f + g)(x) = f(x) + g(x) and g(x) = 4 x – 2. Find (f + g)(x).
COMBINING FUNCTIONS Example: Let f(x) = x 2 + 1 and (f + g)(x) = f(x) + g(x) = x 2 + 1 + 4 x – 2 = x 2 + 4 x – 1 g(x) = 4 x – 2. Find (f + g)(x).
COMBINING FUNCTIONS Example: Let f(x) = 3 x 2 – 5 (f + g)(x) = f(x) + g(x) and g(x) = 6 x – 1. Find (f + g)(x).
COMBINING FUNCTIONS Example: Let f(x) = 3 x 2 – 5 and (f + g)(x) = f(x) + g(x) = 3 x 2 – 5 + 6 x – 1 = 3 x 2 + 6 x – 6 g(x) = 6 x – 1. Find (f + g)(x).
COMBINING FUNCTIONS Example: Let f(x) = x 2 (f – g)(x) = f(x) – g(x) and g(x) = 2. Find (f – g)(x).
COMBINING FUNCTIONS Example: Let f(x) = x 2 (f – g)(x) = f(x) – g(x) = x 2 – 2 and g(x) = 2. Find (f – g)(x).
COMBINING FUNCTIONS Example: Let f(x) = x 2 + 1 (f – g)(x) = f(x) – g(x) and g(x) = 4 x – 2. Find (f – g)(x).
COMBINING FUNCTIONS Example: Let f(x) = x 2 + 1 and (f – g)(x) = f(x) – g(x) = x 2 + 1 – (4 x – 2) = x 2 + 1 – 4 x + 2 = x 2 – 4 x + 3 g(x) = 4 x – 2. Find (f – g)(x).
COMBINING FUNCTIONS Example: Let g)(x). f(x) = 6 x 2 + 3 x – 1 (f – g)(x) = f(x) – g(x) and g(x) = -2 x 2 – 4 x + 2. Find (f –
COMBINING FUNCTIONS Example: Let g)(x). f(x) = 6 x 2 + 3 x – 1 and g(x) = -2 x 2 – 4 x + 2. (f – g)(x) = f(x) – g(x) = 6 x 2 + 3 x – 1 – (-2 x 2 – 4 x + 2) = 6 x 2 + 3 x – 1 + 2 x 2 + 4 x – 2 = 8 x 2 + 7 x – 3 Find (f –
COMBINING FUNCTIONS Example: Let f(x) = 3 x (f * g)(x) = f(x) * g(x) and g(x) = 4 x. Find (f * g)(x).
COMBINING FUNCTIONS Example: Let f(x) = 3 x (f * g)(x) = f(x) * g(x) = 3 x * 4 x = 12 x 2 and g(x) = 4 x. Find (f * g)(x).
COMBINING FUNCTIONS Example: Let f(x) = 7 x + 1 (f * g)(x) = f(x) * g(x) and g(x) = -2 x + 3. Find (f * g)(x).
COMBINING FUNCTIONS Example: Let f(x) = 7 x + 1 and (f * g)(x) = f(x) * g(x) = (7 x + 1)(-2 x + 3) = -14 x 2 + 19 x + 3 g(x) = -2 x + 3. Find (f * g)(x).
COMBINING FUNCTIONS Example: Let f(x) = x 2 + 1 (f * g)(x) = f(x) * g(x) and g(x) = 4 x – 2. Find (f * g)(x).
COMBINING FUNCTIONS Example: Let f(x) = x 2 + 1 and (f * g)(x) = f(x) * g(x) = (x 2 + 1)(4 x – 2) = 4 x 3 – 2 x 2 + 4 x – 2 g(x) = 4 x – 2. Find (f * g)(x).
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