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Warm up

Warm up. Find the slope of the line passing through (-2,0) and (3,1) Write the equation of a line that has a slope of 3 and passes through the point (1,-2) Does the list of ordered pairs below represent a function? Why or why not? (2,11),(2,10),(3,8), (4,5),(5,1). Relations and functions.

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Warm up

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  1. Warm up Find the slope of the line passing through (-2,0) and (3,1) Write the equation of a line that has a slope of 3 and passes through the point (1,-2) Does the list of ordered pairs below represent a function? Why or why not? (2,11),(2,10),(3,8), (4,5),(5,1)

  2. Relations and functions EQ: how do you identify relations and functions?

  3. Vocabulary • Relation: mapping or pairing of input values with output values. A relation may be described by a set of ordered pair, graph, mapping diagram, equation or verbal sentence Examples: (0,-2), (0,2), (3,-1), (3,1). The area A of a circle is related to its radius r by the equation A=

  4. Domain: Set of all input or x values • Range: set of all output or y values • Function: A relation is a function if each input value has exactly one output.

  5. Function Notation • If there is a correspondence between values of the domain, x, and values of the range, y, that is a function, then y = f(x), and (x,y) can be written as (x,f(x)). • The variable x is called the independent variable. • The variable y, or f(x) is called the dependent variable. • Although f is usually used to represent a function, other letters can also be used.

  6. Representing Functions • Verbally: using a sentence to describe how the input variable is related to the output variable. • Numerically: Using a table or list of ordered pairs matching input values with output values. • Algebraically: using an equation in two variables • Graphically: points on a graph. Input values are represented on the x-axis, and output values on the y-axis.

  7. Examples FunctionNot a function

  8. Testing for functions • Which of the following equations represent y as a function of x? • 2x-y-3=0 • Y= 3. –x+y =1

  9. Evaluating Functions • Let g(y)=7-3y; find g(0), g( ), g(s+2) • Evaluate f(x) = –2.5x + 11, where x = –1.

  10. Application • A gift shop sells a specialty fruit and nut mix at a cost of $2.99 per pound. During the holiday season, you can buy as much of the mix as you like and have it packaged in a decorative tin that costs $4.95. a.) Write a linear function to model the total cost in dollars, c, of the tin containing the fruit and nut mix as a function of the number of pounds of the mix, n. b.) ) Find the total cost of a tin that contains 1.5 pounds of the mix.

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