Direct Variation and Graphing Linear Functions

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Presentation transcript:

Direct Variation and Graphing Linear Functions

4.6 Direct Variation Direct Variation modeled by y = mx, book uses y = ax. b = 0 in direct variation. Constant of Variation: fancy word for slope in a direct variation equation.

Examples of Direct Variation y = 2x, constant of variation is 2 y = ¾x, constant of variation is ¾

Examples: Determine if Direct Variation is Represented Examples: Determine if Direct Variation is Represented. If so, Identify the Constant of Variation. 2x – 3y = 0 -x + y = 4 2x + y = 0 -5x + 4y = 20

Graphing Direct Variation y = 2x y = - ½x

Example 3

Extra Example 3

Example 4

Homework 4.6 Page 256: 3 – 8, 12 – 18 evens, 24 – 34 evens, 40 - 42

4.7 Function Notation

4.7 Graph Linear Functions Function notation: y is replaced with f(x). f(x) is read “f of x” f is NOT a variable. y = 2x + 1 and f(x) = 2x + 1 are the same graph.

Evaluating a function Evaluate f(x) = 3x – 15 when x = -3. Ignore f(x), just plug in -3 for x. f(-3) = 3(-3) – 15 f(-3) = -24 Note: this represents the point (-3, -24) on the graph.

Examples Evaluate the function h(x) = -7x when x = 7. Evaluate the function f(x) = 2x + 12 when x = -8

Finding an x-value For the function f(x) = 2x – 10, find the value of x so that f(x) = 6.

Extra Example For the function f(x) = -2x + 4, find the value of x so that f(x) = 16.

Graphing Functions Change the f(x) back to y (if needed) and graph as normal. Graph f(x) = x + 7 Compare to f(x) = x

Graph f(x) = x + 3 h(x) = 2x Compare both to f(x) = x.

Example 5 A cable company charges new customers $40 for installation and $60 per month for its service. The cost to the customer is given by the function f(x) = 60x + 40 where x is the number of months of service. To attract new customers, the cable company reduces the installation fee to $5. A function for the cost with the reduced installation fee is g(x) = 60x + 5. Graph both functions. How is the graph of g related to the graph of f?

Review What does f(x) mean?

Homework Page 265: 4, 6, 12 – 34 evens, 42-44