Daily Check 102510 Write in decimal form Write

Daily Check (10/25/10) Write in decimal form. Write in scientific notation. Simplify. Write your answer in scientific notation.

EOCT Practice Question of the Day

EOCT Practice Beatriz entered her collie in a dog show. During the main event, she will walk in a 129° arc in front of the judges. If the arc were to continue in a circle, its radius would be 3. 5 feet. What is the distance Beatriz and her dog will need to walk (find the arc length)? Round your answer to the nearest hundredth. Use a) b) c) d) 3. 50 feet 7. 00 feet 7. 88 feet 15. 75 feet

Math II Day 52 (10 -25 -10) Standard MM 2 A 5. a Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range. Today’s Question: How do you find the inverse of a function?

4. 3 Inverse Functions p. 116 -119

Review • Relation – a mapping of input values (x-values) onto output values (y-values). • Here are 3 ways to show the same relation. y= x 2 Equation Table of values Graph x y -2 4 -1 1 0 0 1 1

• Inverse relation – just think: switch the x & y-values. x = y 2 ** the inverse of an equation: switch the x & y and solve for y. x y 4 -2 1 -1 0 0 1 1 ** the inverse of a table: switch the x & y. ** the inverse of a graph: the reflection of the original graph in the line y = x.

Switch the X and Y y = 5 x + 3 x = 5 y + 3 x - 3 = 5 y x-3=y 5 5

Let’s try together y = 2 x + 4 x = 2 y + 4 x - 4 = 2 y x-4=y 2 x-2=y 2

y = 2 x + 4 (1/2)x - 2 = y y=x

y = 2 x + 4 (1/2)x - 2 = y x y -5 -6 -6 5 -2 0 0 -2 1 6 6 1 2 8 8 2 5 14 14 5

You try……. Find the inverse of y = 3 x and graph it

Let’s try together y = x 2 + 4 x = y 2 + 4 x - 4 = y 2 x-4=y

y = x 2 + 4 x-4=y

Function • For every value of X there is only 1 corresponding value of Y. or • No Y’s share the same X or • No X’s have more than one Y

Vertical Line Test • Used to determine whether a graph is a function. • If the original function passes the vertical line test, then a function • If the original function does not pass the vertical line test, then it is not a function

Ex: Graph the function f(x)=x 2 and determine whether it is a function. Graph passes the vertical line test, therefore it is a function.

Ex: Graph the function f(x)=x 2 and determine whether it is a function. Graph fails the vertical line test, therefore it is not a function.

Horizontal Line Test • Used to determine whether a function’s inverse will be a function by seeing if the original function passes the horizontal line test • If the original function passes the horizontal line test, then its inverse is a function • If the original function does not pass the horizontal line test, then its inverse is not a function

Ex: Graph the function f(x)=x 2 and determine whether its inverse is a function. Graph does not pass the horizontal line test, therefore the inverse is not a function.

Ex: g(x)=2 x 3 Inverse is a function!

4 Corners Stations • Graph each function and it’s inverse • Tell if the inverse is a function

Homework PG 118 #1 – 6, 9, 10