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Definition
| Every value in the range is matched to only one value in x. |
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| Not every value in the range is matched to only one value in x. |
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| Define Horizontal Line Test |
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Definition
| a method that can be used to determine if a function is a one-to-one function. This means that, for every y-value in the function, there is only one unique x-value |
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| How Does a Graph Pass The Horizontal Line Test? |
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Definition
| Each Horizontal line on the graph only passes through a single point. |
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What does
g(x)=x^2-1
Look Like? |
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Definition
| A parabola that is shifted down one |
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Would
g(x)=x^2-1
Pass the Horizontal Line Test? |
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| line or curve that approaches a given curve arbitrarily closely |
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| f^-1, f^-1(y) =x if and only if y=f(x) |
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If
f(3)=5
is a one to one function
Then the Inverse is... |
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Definition
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| What are the two properties of inverse functions? |
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Definition
(fof^-1)(x)=f(f^-1(x))=x
(f^-1of)(x)=f^-1(f(x))=x |
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| How do you see if f(x) and g(x) are inverse? |
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Definition
1.) Solve (fog)(x)
2.) Solve (gof)(x)
3.) If (fog)(x) and (gof)(x) equal then they are inverses.
4.) If (fog)(x) and (gof)(x) do not equal then they are not inverses of eachother. |
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| Are f(x)=2x+3 and g(x)=(x-3)/2 inverses, and if so why? |
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Definition
| Yes, because (fog)(x) and (gof)(x) are equal. |
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| The graph of the function (f) and the graph of (f^-1) are symmetric with respect to the line.... |
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Definition
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Definition
| The graph of the function (f) and the graph of (f^-1) are symmetric with respect to the line y=x |
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| What are the four steps to finding the Inverse Algebraically? |
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Definition
1.) Replace f(x) by y in the equation for f(x)
2.) Switch x and y
3.) Solve Equation in step 2 for y
4.) Replace y with f^-1(x) |
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| What is the first step to finding the Inverse Algebraically? |
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Definition
| Replace f(x) by y in the equation for f(x) |
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| What is the second step to finding the Inverse Algebraically? |
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Definition
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| What is the third step to finding the Inverse Algebraically? |
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Definition
| Solve Equation in step 2 for y |
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| What is the fourth step to finding the Inverse Algebraically? |
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Definition
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| The domain of your inverse is the ____ of the original function |
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Definition
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| If something has to be greater than or equal to zero then.... |
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Definition
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| Are even functions ever one to one? |
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Definition
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Definition
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| How do You Find the Domain? |
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Definition
Search for restrictions in the function like radicals or variables in the denominator.
Other limitations include how a graph appears. |
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