AA3-0(2) graphing inverses cloned 1/19/2021

In investigation AA3-0 we saw how inverse functions "undo" each other. In this investigation we will look at the graphs of inverse functions and determine how to identify if two functions are inverses and write the equations of inverse functions.

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Graph the inverse functions: f(x) = 2x + 8 and f ^-1(x)= 1/2 x - 4 below.

Objavili smo novi i poboljšani tip pitanja za grafički prikaz! Studenti više neće moći odgovoriti na ovo pitanje.

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Where is the point of intersection?

To your graph above, add the line y=x (you can use the settings to make it a dashed line).

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Graphs of inverse functions are reflections over the line y=x. For that reason, they will intersect at points where x and y are the same number, like (-8,-8).
What does that mean about other points? Notice the point (-4,0) is on f(x). What point on f^-1(x) is the reflection of (-4,0)?

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Notice the x and y values of inverses are reversed. In other words, if the point (a,b) is on the function, (b,a) will be on the inverse function.
We can use this to find the equation of an inverse function from a graph.
Graph g(x) = 5x - 3 below.

Objavili smo novi i poboljšani tip pitanja za grafički prikaz! Studenti više neće moći odgovoriti na ovo pitanje.

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Which of these points will be on the graph of g^-1(x)? (select all)

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Which TWO are equations of g^-1(x) in point-slope form.

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To examine how this works for functions that are not linear we will look at these inverse functions:
What is the vertex of f(x)?

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What is the vertex of f^-1(x)?

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Graph:
and the line y=x below.

Objavili smo novi i poboljšani tip pitanja za grafički prikaz! Studenti više neće moći odgovoriti na ovo pitanje.

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The two graphs are reflections over the line y=x.

Tačno

Netačno

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Are the points reversed between the two functions?

Only the two vertex have reversed points.

Some of the points are reversed, some are not reversed.

Yes, but only half of the points are on the radical function.

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Why are the graphs not perfect reflections of each other?

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When a=1 we can write inverse functions just by identifying the vertex.
What would be the inverse function of

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AA3-0(2) graphing inverses cloned 1/19/2021

Graph the inverse functions: f(x) = 2x + 8 and f -1(x)= 1/2 x - 4 below.

Where is the point of intersection?

Graphs of inverse functions are reflections over the line y=x. For that reason, they will intersect at points where x and y are the same number, like (-8,-8). What does that mean about other points? Notice the point (-4,0) is on f(x). What point on f -1(x) is the reflection of (-4,0)?

Notice the x and y values of inverses are reversed. In other words, if the point (a,b) is on the function, (b,a) will be on the inverse function. We can use this to find the equation of an inverse function from a graph.Graph g(x) = 5x - 3 below.

Which of these points will be on the graph of g-1(x)? (select all)

Which TWO are equations of g-1(x) in point-slope form.

To examine how this works for functions that are not linear we will look at these inverse functions: What is the vertex of f(x)?

What is the vertex of f-1(x)?

Graph: and the line y=x below.

The two graphs are reflections over the line y=x.

Are the points reversed between the two functions?

Why are the graphs not perfect reflections of each other?

When a=1 we can write inverse functions just by identifying the vertex.What would be the inverse function of

Graph the inverse functions: f(x) = 2x + 8 and f -1(x)= 1/2 x - 4 below.

Where is the point of intersection?

Graphs of inverse functions are reflections over the line y=x. For that reason, they will intersect at points where x and y are the same number, like (-8,-8). What does that mean about other points? Notice the point (-4,0) is on f(x). What point on f -1(x) is the reflection of (-4,0)?

Notice the x and y values of inverses are reversed. In other words, if the point (a,b) is on the function, (b,a) will be on the inverse function. We can use this to find the equation of an inverse function from a graph.Graph g(x) = 5x - 3 below.

Which of these points will be on the graph of g-1(x)? (select all)

Which TWO are equations of g-1(x) in point-slope form.

To examine how this works for functions that are not linear we will look at these inverse functions: What is the vertex of f(x)?

What is the vertex of f-1(x)?

Graph: and the line y=x below.

The two graphs are reflections over the line y=x.

Are the points reversed between the two functions?

Why are the graphs not perfect reflections of each other?

When a=1 we can write inverse functions just by identifying the vertex.What would be the inverse function of

Graph the inverse functions: f(x) = 2x + 8 and f ^-1(x)= 1/2 x - 4 below.

Graphs of inverse functions are reflections over the line y=x. For that reason, they will intersect at points where x and y are the same number, like (-8,-8).
What does that mean about other points? Notice the point (-4,0) is on f(x). What point on f^-1(x) is the reflection of (-4,0)?

Notice the x and y values of inverses are reversed. In other words, if the point (a,b) is on the function, (b,a) will be on the inverse function.
We can use this to find the equation of an inverse function from a graph.
Graph g(x) = 5x - 3 below.

Which of these points will be on the graph of g^-1(x)? (select all)

Which TWO are equations of g^-1(x) in point-slope form.

To examine how this works for functions that are not linear we will look at these inverse functions:
What is the vertex of f(x)?

What is the vertex of f^-1(x)?

Graph:
and the line y=x below.

When a=1 we can write inverse functions just by identifying the vertex.
What would be the inverse function of

Graph the inverse functions: f(x) = 2x + 8 and f ^-1(x)= 1/2 x - 4 below.

Graphs of inverse functions are reflections over the line y=x. For that reason, they will intersect at points where x and y are the same number, like (-8,-8).
What does that mean about other points? Notice the point (-4,0) is on f(x). What point on f^-1(x) is the reflection of (-4,0)?

Notice the x and y values of inverses are reversed. In other words, if the point (a,b) is on the function, (b,a) will be on the inverse function.
We can use this to find the equation of an inverse function from a graph.
Graph g(x) = 5x - 3 below.

Which of these points will be on the graph of g^-1(x)? (select all)

Which TWO are equations of g^-1(x) in point-slope form.

To examine how this works for functions that are not linear we will look at these inverse functions:
What is the vertex of f(x)?

What is the vertex of f^-1(x)?

Graph:
and the line y=x below.

When a=1 we can write inverse functions just by identifying the vertex.
What would be the inverse function of