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Function Notation & Direct Variation Date: Function Notation: The equation y = 3x means that y is a “function” of x y = f(x) Can be written as f(x) = 3x This is “f of x” (not f times x) The f can be replaced with any letter such as h(x), g(x), etc. Functions take one value from the domain(x values) and assigns it to a value in the range(y values) Examples: 1. If f(x) = 4x – 2, evaluate f(1) a. Substitute 1 in for x in the equation and solve for f(x) f(x) = 4x – 2 = 4(1) – 2 = 4–2 = 2 2. Evaluate g(-2), if g(x) = 1 x +2 2 3. Evaluate the given function for f(3), if f(x) = x2 – 5x. 4. If h(x) = -x + 3 and h(x) = 12, what is the value of x? a. Set the two functions equal to each other and solve for x *** On graphing calculator *** Y1 = -x + 3 Y2 = 12 2nd Calc intersect Check window – Move to y max = 20 Intersect point is the answer Direct Variation Direct variation occurs when y = mx+ b, b = 0 (line passes through origin) m≠0 Becomes y = mx m(or slope) is the constant of variation So we now have y = kx (recall k was constant of variation in chapter 6) y Solving for k, we get k = x Examples: Solve for y y = 7x 1. y = 7x Is the equation in the form y = kx? Yes Is it a direct variation? Yes Constant of Variation 7 2. y = 4x – 10 3. 5x – 2y = 0 Complete the table: y for x each ordered pair Find the value of x y 10 2 15 3 20 4 x y 4 16 8 20 12 24 y the same x for each ordered pair? Is the value of Direct Variation? Word Problems Set up as a proportion 1. The number of miles driven varies directly with the number of gallons of gas used. Erin drove 297 miles on 9 gallons of gas. How far would she be able to drive on 14 gallons of gas? 2. The number of people that can be seated in a lecture hall varies directly with the number of rows of seats. If 72 people can be seated in 4 rows, how many people can be seating in 13 rows? Homework: pg. 228 1 & 2 (a, e, g only), 3, 4, 5 pg. 230 1a, b, c, d, 2, 4, 7 – 13 odds