Dr. Fowler  AFM  Unit 1-2 The Graph of a Function

EXAMPLE – Identifying the Graph of a Function: Theorem – Vertical line TEST… A set of points in the xy-plane is the graph of a function if and only if every vertical line intersects the graph in at most one point. EXAMPLE – Identifying the Graph of a Function: Which of the following are graphs of functions? A Function A Function

EXAMPLE – Identifying the Graph of a Function: Which of the following are graphs of functions? Not A Function Not A Function

ƒ(x) = 5x + 3 ƒ(1) = 5(1) + 3 Evaluating Functions: Output value Input value Output value Input value ƒ(x) = 5x + 3 ƒ(1) = 5(1) + 3 ƒ of x equals 5 times x plus 3. ƒ of 1 equals 5 times 1 plus 3. f(x) is not “f times x” or “f multiplied by x.” f(x) means “the value of f at x.” So f(1) represents the value of f at x =1 Caution

The function described by ƒ(x) = 5x + 3 is the same as the function described by y = 5x + 3. And both of these functions are the same as the set of ordered pairs (x, 5x+ 3). y = 5x + 3 (x, y) (x, 5x + 3) Notice that y = ƒ(x) for each x. ƒ(x) = 5x + 3 (x, ƒ(x)) (x, 5x + 3) The graph of a function is a picture of the function’s ordered pairs.

Video - Evaluating Functions: https://www. youtube. com/watch Pay close attention. Take Notes.

Example 1A: Evaluating Functions For each function, evaluate ƒ(0), ƒ , and ƒ(–2). ƒ(x) = 8 + 4x Substitute each value for x and evaluate. ƒ(0) = 8 + 4(0) = 8 ƒ = 8 + 4 = 10 ƒ(–2) = 8 + 4(–2) = 0

Example 1B: Evaluating Functions For each function, evaluate ƒ(0), ƒ , and ƒ(–2). Use the graph to find the corresponding y-value for each x-value. ƒ(0) = 3 ƒ = 0 ƒ(–2) = 4

For each function, evaluate ƒ(0), ƒ , and ƒ(–2). Example – LET US ALL TRY THIS BY OURSELVES: For each function, evaluate ƒ(0), ƒ , and ƒ(–2). ƒ(x) = –2x + 1

Example Graph the function. 3 5 7 9 2 6 10 Graph the points. Do not connect the points because the values between the given points have not been defined.

NOTES: In the notation ƒ(x), ƒ is the name of the function NOTES: In the notation ƒ(x), ƒ is the name of the function. The output ƒ(x) of a function is called the dependent variable because it depends on the input value of the function. The input x is called the independent variable. When a function is graphed, the independent variable is graphed on the horizontal axis and the dependent variable is graphed on the vertical axis.

Find X Min-Max Find Y Min-Max Four times.

Yes

What are the x- and y-intercepts? The x-intercept is where the graph crosses the x-axis. The y-coordinate is always 0 for the x-intercept. The y-intercept is where the graph crosses the y-axis. The x-coordinate is always 0 for the y-intercept. (2, 0) (0, 6)

Find the x- and y-intercepts. 1. x - 2y = 12 x-intercept: Plug in 0 for y. x - 2(0) = 12 x = 12; (12, 0) y-intercept: Plug in 0 for x. 0 - 2y = 12 y = -6; (0, -6)

Excellent Job !!! Well Done