Consider the function g(x)=-x. a. Graph g(x)=-x and explain why it is its own inverse. Also verify that g(x)=g^-1(x) algebraically. b. Graph other linear functions that are their own inverses. Write equations of the lines you graphed. c. Use your results from part (b) to write a general equation describing the family of linear functions that are their own inverses. | Numerade
Consider the function g(x)=-x. a. Graph g(x)=-x and explain why it is its own inverse. Also verify that g(x)=g^-1(x) algebraically. b. Graph other linear functions that are their
Consider the function g(x)=-x. a. Graph g(x)=-x and explain why it is its own inverse. Also verify that g(x)=g^-1(x) algebraically. b. Graph other linear functions that are their own inverses. Write equations of the lines you graphed. c. Use your results from part (b) to write a general equation describing the family of linear functions that ...
numerade.com1 个月前
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Inverse functions discovery— here’s a simple, hands-on idea for introducing inverse functions. It can also be used to discover geometric transformations over y = x. All you need is a square coordinate grid, a hole punch and a pencil or pen. Recording all class data on the whiteboard as a class may be fun to do, too. Students will start to see that x and y swap spots in inverses. The hole punch I’m using here is 1/8th-inch with a 2-inch reach. #inversefunctions #geometrictransformations #teaching
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Inverse functions discovery— here’s a simple, hands-on idea for introducing inverse functions. It can also be used to discover geometric transformations over y = x. All you need is a square coordinate grid, a hole punch and a pencil or pen. Recording all class data on the whiteboard as a class may be fun to do, too. Students will start to see that x and y swap spots in inverses. The hole punch I’m using here is 1/8th-inch with a 2-inch reach. #inversefunctions #geometrictransformations #teaching
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