Write the equation in slope intercept form then

§ Write the equation in slope- intercept form, then graph the new equation. § State whether it is a function or not and why. 1) 2 x+4 y=8 2) 2 x -y=3

y=1/2 x-2 y=x 2 -3

§ A relationship between variables. § How do we recognize a function? You can identify a function with the vertical line test. For every input there can only be one output.

§ A function is one-to-one if it passes the vertical and horizontal.

We use inverses to solve and interpret equations.

§ Find the inverse of a function § Find the inverse of a relation § Graph a function and it’s inverse § Identify quadratic and square root functions § Understand the relationship between a function and it’s inverse

§ An inverse function is a function that undoes the action of another function. A function g is the inverse of a function f when y=f(x) then x= g(y). § Switch x and y then solve for y. § f-1 is the notation we use for the inverse of f. § Example f(x)=2 x+3 find f-1(x)

§ y=4 x-5 y=1/2 x+4 f(x)=x 2

§ A set of ordered pairs. § { (1, 2), (2, 3), (3, 4), (4, 5) } § A relation is a function when each input is paired with only one output or when every x-value is paired with only one y-value § Examples 1) { (2, 4), (3, 6), (4, 8), (5, 10) } 2) { (1, 1), (2, 2), (2, 3), (4, 5) } 3) { (-3, 5), (-4, -5), (-5, 5), (-6, -5) }

§ An inverse relation is the relation that occurs when the order of the elements are switched in the relation. § Example: Given the relation { (0, 7), (4, -3), (-3, 4), (-2, -2) }, find the inverse relation.

§ A linear function is the inverse of a linear function, a quadratic function is the inverse of a square root function § When you find the inverse of a square root or quadratic function, you must restrict the range so that y>0. § Domain of the relation becomes the range of the inverse and the range of the relation becomes the domain of the inverse. § Check your answer by creating a table and checking that the original function and the inverse function are symmetric about y=x.

f(x)=x+4

f(x)=x 2+1

We will discuss the inverse of exponential and logarithmic functions and use the inverse relationship to solve problems.