3-2 Representing Functions Algebra 1 Glencoe McGraw-Hill Linda Stamper

Some relations are functions. Tri 1 Report Card In a function, each member of the domain is paired with exactly one member of the range. Period Grade 1 4 2 3 5 6 x(domain) y(range) 1 4 2 3 5 6 Could you have more than one grade for Period 1? Alphabetical order: domain listed before range! A=4 B=3 C=2 D=1 F=0

I purchased the following items at the store. Nike Soccer Store Item Price 1 12 2 24 5 26 {(1,12), (2,24), (5,26), (1,12), (5,26), (5,26)} Is the relation a function? Yes, it is a function, because each member of the domain (item) is paired with exactly one member of the range (price). 1=soccer socks 2=shin guards 3=soccer ball size 3 4=soccer ball size 4 5=soccer ball size 5

Is the relation a function? Explain. Nike Soccer Store Item Price 1 12 2 24 5 26 28 {(1,12), (2,24), (5,26), (1,12), (5,28), (5,26)} No, it is not a function, because item 5 (domain) has more than one price (range). Could you determine whether it is a function by looking at the ordered pairs? 1=soccer socks 2=shin guards 3=soccer ball size 3 4=soccer ball size 4 5=soccer ball size 5

Is the relation a function? Explain. Mapping x y 4 2 -4 -3 1 4 -5 -3 No, it is not a function, because domain 2 has different ranges. {(4,1), (2,4), (-4,1), (2,-5), (0,-3), (-3,-3)}

Example 1 Is the relation a function? Explain. domain range -2 2 -1 1 Yes, it is a function, because for each domain there is only one range.

Example 2 Is the relation a function? Explain. domain range 2 1 4 6 3 Yes, it is a function, because for each domain there is only one range.

Example 3 Is the relation a function? Explain. domain range 2 4 1 6 -1 No, it is not a function, because domain 4 has different ranges.

Example 4 Is the relation a function? Explain. domain range 3 9 6 18 27 12 36 {(3,9), (6,18), (9,27), (3,9), (12,36)} Yes, it is a function, because each domain has one range.

Example 5 Is the relation a function? Explain. domain range -3 12 -2 8 -1 4 -12 {(-3,12), (-2,8), (-1,4), (0,0), (-1,4), (-2,8),(-3,-12)} No, it is not a function, because domain -3 has two ranges.

Next you will learn how to identify whether a graph is a function. When you graph a function, the domain is given by the horizontal axis and the range is given by the vertical axis. y (range) x (domain) The x is usually called the independent variable and the y is the dependent variable.

A vertical line test is used to determine whether a graph represents a function. A graph is a function if any vertical line intersects the graph at no more than one point. y (range) x (domain) The line is the graph (do not confuse the coordinate plane as the graph)! The graph is a function.

You can use your pencil to check You can use your pencil to check. Keep your pencil straight to represent a vertical line and pass it across the graph. If it touches the graph at more than one point, the graph is not a function. y (range) x (domain)

The graph is NOT a function. A vertical line test is used to determine whether a graph represents a function. A graph is a function if any vertical line intersects the graph at no more than one point. y (range) x (domain) The graph is NOT a function.

A vertical line test is used to determine whether a graph represents a function. A graph is a function if any vertical line intersects the graph at no more than one point. y (range) x (domain) The graph is a function.

The graph is NOT a function. A vertical line test is used to determine whether a graph represents a function. A graph is a function if any vertical line intersects the graph at no more than one point. y (range) x (domain) The graph is NOT a function.

The graph is NOT a function. A vertical line test is used to determine whether a graph represents a function. A graph is a function if any vertical line intersects the graph at no more than one point. y (range) x (domain) The graph is NOT a function.

You can use your pencil to check You can use your pencil to check. Keep your pencil straight to represent a vertical line and pass it across the graph. If it touches the graph at more than one point, the graph is not a function. y (range) x (domain) The graph is a function.

The graph is NOT a function. You can use your pencil to check. Keep your pencil straight to represent a vertical line and pass it across the graph. If it touches the graph at more than one point, the graph is not a function. y (range) x (domain) The graph is NOT a function.

Function Notation: When a function is defined by an equation, it is often convenient to name the function. Just as x is commonly used as a variable, the letter f is commonly used to name a function. To write a function notation, you use f(x) in place of y. The symbol f(x) is read as “the value of f at x” or simply “f of x”. It does not mean f times x. x-y notation function notation

Remember: If you see f(x), g(x), h(x) or any variable _(x) it is the name for the function and it is used in place of y.

Think of f(x) as the formal name for y. Given f(x) = 3x – 2 find f(–4). Write the function. y Substitute. Simplify (right side only)! Think of f(x) as the formal name for y.

Think of g(x) as the formal name for y. Given g(x) = 3x – 2 find g(a - 3). Write the function. y Substitute. Simplify (right side only)! Think of g(x) as the formal name for y.

Example 6 Given f(x) = –3x + 7 find f(4). Example 7 Given find g(-21). Example 8 Given find h(4). Example 9 Given f(x) = –3x + 7 find f(a – 2). Example 10 Given h(x) = x2 – 2x find h(2n).

y y y Example 6 Example 7 Example 8 Think of g(x) as the formal name for y. Think of f(x) as the formal name for y. Think of h(x) as the formal name for y.

Example 9 Given f(x) = –3x + 7 find f(a – 2). Example 10 Given h(x) = x2 – 2x find h(2n).

Example 11 Given f(x) = 3x + 7 find 3[f(r)]. Example 12 Given g(x) = x2 – 2x find 2[g(t)].

Homework 3-A3 Pages 152-154 #15-36,45-47,54-55.