Review: 1. Solve for a: 4 3 = 2 a 2. What is the domain for y = 2e -x - 3? 3. What is the range for y = tan x?

Answers: 3. Domain:(-∞, ∞) Range: (-2,∞) x = (2 4 ) 3x = 2 12x 9. x-intercept:≈ y-intercept: x-intercept: 2.0 y-intercept:≈ c 18. f 21. Use 500,000(1.0375) t = 1,000,000 t ≈ a. A(t) = 6.6(.5) t/14 b. t ≈ Use 2300(1.06) t = 4150 t ≈ Use 2A = A(1.0625) t 2 = t t ≈ Use A( /12) 12t t ≈ Use 2A = Ae.0625t t ≈ a. Use C(t) = 10,000(.8) t t ≈ b. t ≈ x y ratio a.y = (1.0178) t b. 36, 194,000 exceeds actual by 710,000 c. 1.8%

Parametric Equations If x and y are given as the functions x = f(t) y = g(t) over an interval of t-values, then the set of points (x,y) = (f(t),g(t)) defined by these equations is a parametric curve. The equations are giving the horizontal and vertical positions over time.

t as a variable Aside from setting our domain and range, we also need to set the interval of time we are looking at the equations. What value of t should be our starting point? Why would we want to have a negative value for the initial t?

Ex 1: Let x = a cos t and y = a sin t. a) Let a = 1, 2, or 3 and graph the parametric equations in a square viewing window using a parameter interval of [0,2π]. How does changing a affect the graph? b) Let a = 2 and graph the interval over the following parameter values: [0,π/2] 0,π] [0,3π/2] [0,2π] [2π,4π] [0,4π] Describe the role of the length of the parameter values.

Ex 2: Find the Cartesian equation for the parametric equations a) x = t, y = 2t t ≥ 0 b) x = √t, t = t 2, t ≥0

Ex 3: Find the Cartesian equation for the parametric equations a) x = 3 cost t, y = 3 sin t, 0 ≤ t ≤ 2π b) x = 4 cos t, y = 2 sin t, 0 ≤ t ≤2π

Assignment: p 34 # 1-25 odd