1. 2.6 Relations and Parametric Equations Pg. 150#42-44 Pg. 136#9 – 35 odd #25(3, -4)r = 4 #26(1, -3)r = 7 #27(2, -3)r = #28(7, 4)r = #42[-2, -1)U(-1, ∞)#90no symmetry #43(∞, 1]U[4, ∞ )#91origin #48No real solutions#92y – axis, x – axis and origin #88y – axis #93origin #89x – axis

2. 2.6 Relations and Parametric Equations Circles Write the standard form of the equation of a circle from the given information and state the center and radius. Symmetry Practice Determine the type of symmetry for the following equations:

3. 2.7 Inverse Functions Inverse Relations The inverse of relation R, denoted R -1, consists of all those ordered pairs (b, a) for which (a, b) belong to R. In other words, (a, b) is in the relation R if, and only if, (b, a) is in the relation R -1. Graphically, an inverse is a reflection of the original graph over the line y = x. In generic terms, you find an inverse by swapping the x and y and then solving back for the y.

4. 2.7 Inverse Functions Examples Find the inverse of y = 3x + 8 algebraically. Graph the original equation and the inverse along with the line y = x to show it has the proper symmetry. Find the inverse of y = x 2 algebraically. Graph the original equation and the inverse along with the line y = x to show it has the proper symmetry.

5. 2.7 Inverse Functions Examples How is f(x) = x 2 different than y = x 2 ? In order to find an inverse function of f(x) = x 2, we need to set limits on the domain. Inverse Functions In order for an inverse function to exist, first you must be dealing with a function and that function must pass the VLT and the HLT. HLT – Horizontal Line Test (of the original function) is just like the VLT, except it will tell you whether or not the inverse will be a function.

6. 2.7 Inverse Functions Inverse Functions If an inverse and the original function are composed together, they should always equal x. This works for all values of x in the domain of each function. – > f -1 (f(x)) = x – > f(f -1 (x)) = x Examples How is f(x) = x 2 different than y = x 2 ? This fails the HLT, so if you say f(x) = x 2, where x ≥ 0 you are safe! (you can still use y to solve) Find the inverse function and prove it is an inverse function.

7. 2.7 Inverse Functions Inverse Functions Show that f(x) = will have an inverse function. – Find the inverse function and state its domain and range. – Prove that the two are actually inverses. Show that g(x) = will have an inverse function. – Find the inverse function and state its domain and range. – Prove that the two are actually inverses. Show that h(x) = x 3 – 5x will have an inverse function.