1-7 functions Goals: Identify a function. Find function values. Eligible Content: A1.2.1.1.2 / A1.2.1.1.3 / A1.2.1.2.1 / A1.2.1.2.2

Vocabulary Function – relationship between 2 quantities called the input and output, where each input must have only one output.

Different looks of functions Tables Mapping Ordered Pairs Graphs Equations

Tables Input Output 3 1 5 2 7 9 Input Output 1 4 2 3 Input Output 5 1 3 1 5 2 7 9 Input Output 1 4 2 3 Input Output 5 1 2 3 4 Input Output -2 6 5 2 3 4 1 Input Output 3 1 7 9 2 8 Input Output 1 4 2 3 5

Mappings 2 4 6 8 5 3 2 8 8 1 9 yes 2 4 6 yes 6 4 8 9 5 2 8 4 3 6 no 10 yes

Ordered Pairs {(2,4),(3,6),(4,8),(5,10)} {(1,6),(1,2),(3,9),(4,7)} Yes {(1,6),(1,2),(3,9),(4,7)} No {(2,5),(3,5),(4,5),(5,5)} {(4,4),(4,7),(4,9),(4,13)} no

Is this relation a function? Explain. Yes; for each element of the domain, there is only one corresponding element in the range. Yes; it can be represented by a mapping. No; it has negative x-values. No; both –2 and 2 are in the range.

Is this relation a function? Explain. No; the element 3 in the domain is paired with both 2 and –1 in the range. No; there are negative values in the range. Yes; it is a line when graphed. Yes; it can be represented in a chart.

Graphs Vertical Line Test – If a vertical line touches a graph in more than one place it does not represent a function.

Graphs NOT a function

Equations Function Notation – using the symbol f(x) instead of y in an equation. Instead of y = 2x + 1 we write f(x) = 2x + 1 Nonlinear function – a function whose graph is not a straight line. Pronounced “f of x”

Examples Evaluate each function with the given value. f(x) = 2x – 3, find f(-2). f(-2) = -7 g(x) = -5x, find g(0). g(0) = 0 h(x) = 1248 – 160x + 16x2, find h(3). h(3) = 912

If f(x) = 2x + 5, find f(3). A. 8 B. 7 C. 6 D. 11

The function h(t) = 180 – 16t2 represents the height of a ball thrown from a cliff that is 180 feet above the ground. A. Find h(2). A. 164 ft B. 116 ft C. 180 ft D. 16 ft

Practice Worksheet – “1-7 Skills Practice”

Homework Page 52 #20-25, 27, 28, 33-36