Warm Up Evaluate each expression for a = 2, b = –3, and c = a + 3c 2. ab – c c + b 4. 4c – b 5. b a + c 26 – x + y = 3 Solve each equation for y. 7. – x + 3y = – x – 2y = 8 y = – 2x + 3 y = 2x – 4

A function is a special type of relation that pairs each domain value with exactly one range value. In other words, for every input (x value), there is exactly one output (y value). 4-6: Functions

Example 1: Identifying Functions Give the domain and range of the relation. Tell whether the relation is a function. Explain. {(3, –2), (5, –1), (4, 0), (3, 1)} R: {–2, –1, 0, 1} D: {3, 5, 4} Even though 3 is in the domain twice, it is written only once when you are giving the domain. The relation is not a function. Each domain value does not have exactly one range value. The domain value 3 is paired with the range values –2 and 1.

–4 – D: {–4, –8, 4, 5} R: {2, 1} Use the arrows to determine which domain values correspond to each range value. This relation is a function. Each domain value is paired with exactly one range value. Additional Example 1B: Identifying Functions Give the domain and range of the relation. Tell whether the relation is a function. Explain. X Y

Give the domain and range of each relation. Tell whether the relation is a function and explain. X Y Example 1c a. {(8, 2), (–4, 1), (–6, 2),(1, 9)} b. The relation is not a function. The domain value 2 is paired with both –5 and –4. D: {–6, –4, 1, 8} R: {1, 2, 9} The relation is a function. Each domain value is paired with exactly one range value. D: {2, 3, 4} R: {–5, –4, –3}

3. Give the domain and range of the relation. Tell whether the relation is a function. Explain. X Y Mini Lesson Quiz: Part I D: {5, 10, 15}; R: {2, 4, 6, 8}; The relation is not a function since 5 is paired with 2 and 4.

What is the “Vertical Line Test” ?

   Example 2A The three points below form a straight line, thus this appears to be the graph of a linear function. Use the vertical line test on the graph. No vertical line will intersect the graph more than once. The equation – 3x + 2 = y represents a function.

Example 2B The points below appear to form a V-shaped graph. Draw two rays from (0, 2) to show all the ordered pairs that satisfy the function. Draw arrowheads on the end of each ray. Use the vertical line test on the graph.    No vertical line will intersect the graph more than once. The equation y = |x| + 2 represents a function.

Functions can be named with any letter; f, g, and h are the most common. You read f(6) as “f of 6,” and g(2) as “g of 2.” Reading Math

Evaluation of Functions: Example 4 Evaluate the function for the given input values. For h(c) = 2c – 1, find h(c) when c = 1 and when c = –3. h(c) = 2c – 1 h(1) = 2(1) – 1 = 2 – 1 = 1 h(c) = 2c – 1 h(–3) = 2( – 3) – 1 = –6 – 1 = – 7

Example 4b Evaluate each function for the given input values. 4. For g(t) = find g(t) when t = 20 and when t = – 12. g(20) = 2 g( – 12) = – 6 5. For f(x) = 6x – 1, find f(x) when x = 3.5 and when x = – 5. f(3.5) = 20 f( – 5) = – 31