Domain of Functions Algebraically

Combine the given equations using the appropriate operation, then simplify by collecting like terms. Example 1: Given the discrete functions below, find: f(x) = {(1, 4), (2, -3), (3, 0), (4, 2), (5, -1)} g(x) = {(1, 6), (3, 7), (5, -3), (7, 1), (9, -4)} a) (f + g)(x) Remember to consider the domain of each function!

• {(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)}

Combine the given equations using the appropriate operation, then simplify by collecting like terms. Example 1: Given the discrete functions below, find: f(x) = {(1, 4), (2, -3), (3, 0), (4, 2), (5, -1)} g(x) = {(1, 6), (3, 7), (5, -3), (7, 1), (9, -4)} b) (f - g)(x) Remember to consider the domain of each function!

• {(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)

Combine the given equations using the appropriate operation, then simplify by collecting like terms. Example 2: Given f(x) = -x^2 + 3 and g(x) = -2x, b) Determine the range for (f + g)(x).

• (-∞, 3]

• (-∞, 0]

• [0, ∞)

• [3, ∞)

• frac{1}{28}

• frac{17}{84}

• frac{1}{12}

• \frac{1}{14}

State the domain for the following function:

State the vertical asymptote for the following function:

State the vertical asymptote for the following function:

Algebraically, we can find the vertical asymptotes of rational functions by...

• finding what makes the denominator equal to zero.

• finding what makes the common factors cancelled out equal to zero.