Combination Functions: Sums and Differences of Functions

Only functions that share the __________ can be combined. Therefore, __________ must be considered before combining.

• common characteristics

• same input type

• identical output

• similar purpose

If the functions do not __________ , they cannot be combined.

• share a domain

• have the same range

• intersect at a point

• have the same codomain

Graphically/Table: Achieved by applying the appropriate operation to the __________ of each function that correspond with the same x-value.

• value

• slope

• derivative

• integral

Example 1: Determine (f + g)(x), (f - g)(x), and (g - f)(x) for the following functions. f(x) = 4, g(x) = 2.5.

• (f + g)(x) = 6.5, (f - g)(x) = 1.5, (g - f)(x) = -1.5

• (f + g)(x) = 6.5, (f - g)(x) = 1.5, (g - f)(x) = 1.5

• (f + g)(x) = 6.5, (f - g)(x) = -1.5, (g - f)(x) = 1.5

• (f + g)(x) = 6.5, (f - g)(x) = -1.5, (g - f)(x) = -1.5

Example 2: Determine (f + g)(x) for the following functions. f(x) = x^2, g(x) = sqrt{x}.

• x^2 + sqrt{x}

• x^2 - sqrt{x}

• x^2 * sqrt{x}

• x^2 / sqrt{x}

• {(1, 10), (3, 7), (5, -4)}

• {(1, 10), (3, 7), (5, -1)}

• {(1, 10), (3, 7), (5, -4), (7, 1), (9, -4)}

• {(1, 10), (2, -3), (3, 7), (4, 2), (5, -4)}

• {(1, -2), (3, -7), (5, 2)}

• {(1, -2), (3, -7), (5, 2), (7, 1), (9, -4)}

• {(1, 10), (3, 7), (5, 2)}

• {(1, 10), (3, 7), (5, 2), (7, 1), (9, -4)}

• (1, 2), (3, 7), (5, -3)

• (1, 2), (3, 7), (5, -2)

• (1, 2), (3, 7), (5, -4)

• (1, 2), (3, 7), (5, -1)

• (-∞, 3]

• (-∞, 0]

• [0, ∞)

• [3, ∞)