Inverse of a Linear Function Math Background Previously, you Performed operations with linear functions Identified the domain and range of linear functions In this unit you will a linear equation for a given y value Solve a literal equation for a given variable Find the inverse of a linear function Describe how the domain of a function must be restricted so the function has an inverse You can use the skills in this unit to Find the inverse of a linear function and recognize restrictions on its domain Solve for the independent variable in terms of the dependent variable in real-world situations Read values of an inverse function from a graph or a table, given that the function has an inverse Graph the inverse of a function by reflecting the graph over the line y = x Vocabulary Domain The input values of a relation. – Horizontal line test The inverse of a function is also a function if and only if no horizontal line intersects the – f graph of more than once. f Inverse functions Two functions are inverse functions if the domain of the original function matches the range – of the second function. Inverse relation Interchanges the input and output values of the original relation. – An equation that involves two or more variables. Literal equation – One-to-one function A function whose inverse is a function. Both must pass the vertical and horizontal line – tests The output values of a relation. – A relation is a function if and only if no vertical line intersects the graph of the function more Vertical line test – than once. Essential Questions How is the inverse of a relation related to the relation? How do you find the inverse relation of a function? Overall Big Ideas The inverse of a relation is by reflecting the ordered pairs about the line y = x. Relations can be restricted to “created” force the inverse to be a function. Using Algebra we can find the inverse function for any line.
Inverse of a Linear Function Math Background Previously, you Performed operations with linear functions Identified the domain and range of linear functions In this unit you will a linear equation for a given y value Solve a literal equation for a given variable Find the inverse of a linear function Describe how the domain of a function must be restricted so the function has an inverse You can use the skills in this unit to Find the inverse of a linear function and recognize restrictions on its domain Solve for the independent variable in terms of the dependent variable in real-world situations Read values of an inverse function from a graph or a table, given that the function has an inverse Graph the inverse of a function by reflecting the graph over the line y = x Vocabulary Domain – The input values of a relation. Horizontal line test – The inverse of a function f is also a function if and only if no horizontal line intersects the graph of f more than once. Inverse functions – Two functions are inverse functions if the domain of the original function matches the range of the second function. Inverse relation – Interchanges the input and output values of the original relation. Literal equation – An equation that involves two or more variables. One-to-one function – A function whose inverse is a function. Both must pass the vertical and horizontal line tests – The output values of a relation. Vertical line test – A relation is a function if and only if no vertical line intersects the graph of the function more than once. Essential Questions How is the inverse of a relation related to the relation? How do you find the inverse relation of a function? Overall Big Ideas The inverse of a relation is “created” by reflecting the ordered pairs about the line y = x. Relations can be restricted to force the inverse to be a function. Using Algebra we can find the inverse function for any line.
resource_6523.docx