Topic #2: Understanding Inverse Relations

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Presentation transcript:

Topic #2: Understanding Inverse Relations After completing the topic Understanding inverse relations, students will understand the graphical, tabular, and algebraic relationship between a linear function and its inverse; understand the relationship between exponential and logarithmic functions; understand the relationship between quadratic and square root functions; identify one-to-one functions; be able to restrict the domain of a quadratic function in order for its inverse to be a function.

Finding an Inverse Steps for finding the inverse of a function Change f(x)  y Exchange x and y in the equation Solve the equation for y Replace y with Example: f(x) = 2x – 5

Drill 1. Find the inverse of the function, 2. Then graph the function and its inverse on the same graph. (Label both functions). Graph the line y = x on the same graph to show that the two functions are inverses.

Drill 1. Find the inverse of the function, 2. Then graph the function and its inverse on the same graph. (Label both functions). Graph the line y = x on the same graph to show that the two functions are inverses. Homework: Staple together homework #7, 8, and 9. Due after the drill

Drill 1. Graph the function, (Make a table of values) 2. Identify the domain and range of the function (using the graph) 3. Graph the inverse of the function on the same graph (invert the original table of value) 4. Using the domain and range from #2 to help you, identify the domain and range of the inverse. 5. Identify the equation of inverse.

Drill Find the inverse of the following functions: 1. 2. 3.

Drill Which of the following functions is Quadratic? X Y -2 1 2 3 8 X Y -2 4 -1 7 12 1 19

Topic #2 Review Get out a clean sheet of notebook paper and label it: Topic #2 Review: Understanding Inverse Relations Copy all problems, show all work.