Warm Up Find the VA, HA & intercepts: VA x = -3x = -2 HA y = 0y = 3 Intercepts (0,4/3)(1/3, 0) (0,-1/2)

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Presentation transcript:

Warm Up Find the VA, HA & intercepts: VA x = -3x = -2 HA y = 0y = 3 Intercepts (0,4/3)(1/3, 0) (0,-1/2)

Inverse Functions February 21, 2012

Inverse Functions Two functions are ______________ if and only if one functions contains the point _________ and its inverse contains the point _________. Switch _________ and _________ of the ordered pairs of the function.

Inverse Functions f(x) denotes the ____________ and f -1 (x) denotes the ___________ When graphed: a function and its inverse are _________________ to each other about the line ___________.

Determining Inverse Functions The inverse of f(x) is a function if it passes the HORIZONTAL line test. – Horizontal Line test: an inverse of f(x) is a function if a horizontal line intersects the graph only once at a time.

Determine if the inverse is a function Fails at this point!

Find the inverse { (0,3), (1,6), (2,3), (4,1)} – Inverse: { (3,0), (6,1), (3,2), (1,4)} { (2,1), (-2,4), (4,1), (-4,3)} – Inverse: { (1,2), (4,-2), (1,4), (3,-4)} { (-2,0), (7,-2), (1,5), (3,-4)} – Inverse: { (0,-2), (-2,7), (5,1), (-4,3)} Yes, its REALLY that easy!! All you have to do is switch the x and y values for each ordered pair.

Finding Inverses There are two ways to find inverses of functions: –

Algebraically 1)Rewrite _______________ 2)Switch the _____ and _____ 3)Solve for _____ which is ________ (the inverse of f(x))

Find the inverse. y = 2x – 3 x = 2y – 3 Step 1: Rewrite f(x) as y Step 2: Switch x and y values. Step 3: Solve for y

Find the inverse. y = x 2 – 1 x = y 2 – 1 Step 1: Rewrite f(x) as y Step 2: Switch x and y values. Step 3: Solve for y

Find the inverse. y = 5x 3 – 3 x = 5y 3 – 3 Step 1: Rewrite f(x) as y Step 2: Switch x and y values. Step 3: Solve for y

Find the inverse. Step 1: Rewrite f(x) as y Step 2: Switch x and y values. Step 3: Solve for y

Find the Inverse. Do on your own.

Special Case There is no way to find the inverse of ABSOLUTE VALUE by the algebraic method. This is where GRAPHING comes in. You can use graphing on other functions as well, but you MUST use graphing when looking at absolute value.

Graphing 1)Make a ____________. 2)Switch the ______ and _____ in the ordered pairs.

Graphing Cont. 3) _________ the new pairs and graph the function. 4) Make sure graph of inverse function and the original function are symmetrical to _______.

Graph f(x) and f -1 (x) on the same graph.