U2D4 Inverse Functions Jan28

Akwankyerɛ

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From the video, what is an inverse function?

1

The video makes finding an inverse function look so easy.
What is step 1 to finding an inverse function?

1

From the video, what is step 2 to finding an inverse function?

1

From the video, what is step 3 to finding an inverse function?

Solve for y (isolate y) and replace the y with inverse notation.

Shake it all about.

Add them all together and divide by the Megatron.

Re-watch the video, because you can't remember.

Put your left foot in.

Repeat steps 1 and 2.

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Click on the link and check on all the options to the right.

https://www.geogebra.org/m/vh6cSjSD

Adjust the slider for m (the slope) and b (the y-intercept)- and observe a line and its inverse.

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Check all the options to the right to make it work.
What happens as the slope (m) increases? Describe what happens to both lines.

1

Check all the options to the right to make it work.
What happens as the y-intercept (b) increase? Describe what happens to both lines.

Height and Weight

The formula

approximates the recommended minimum weight in pounds for a person h inches tall, where

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What is the recommended minimum weight for someone 70 inches tall?

1

Does 𝑊 represent a one-to-one function? Explain your reasoning.

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Function or Not?

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The table represents a function C that computes the percentage of the time that the sky is cloudy in Augusta, Georgia, where x corresponds to the standard numbers for the months.

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The table below represents a function C that computes the percentage of the time that the sky is cloudy in Augusta, Georgia, where x corresponds to the standard numbers for the months.
Construct a table of the inverse of this relationship.

1

Determine if the inverse of C(x) is a function. Justify your response.

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Explore

Calories in food provide essential energy, for you as well as your pet. But how much should you be feeding your pet and how does the size and weight of your pet influence the amount of food they need?

The adult weight of your dog is determined by the number of calories you feed your puppy. The function

relates the number of kilocalories per day, k, to the adult weight of the dog (in kilograms), w.

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A graphical way to determine if a function is one-to-one (the inverse is a function) is the Horizontal Line Test. If every horizontal line intersects the graph of a function f at most once, then f is a one-to-one function. In other words, the inverse is also a function.

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Is the following graph one-to-one?

Yes

No

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Does the following graph have an inverse that is a function?

Yes

No

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U2D4 Inverse Functions Jan28

From the video, what is an inverse function?

The video makes finding an inverse function look so easy. What is step 1 to finding an inverse function?

From the video, what is step 2 to finding an inverse function?

From the video, what is step 3 to finding an inverse function?

Check all the options to the right to make it work.What happens as the slope (m) increases? Describe what happens to both lines.

Check all the options to the right to make it work.What happens as the y-intercept (b) increase? Describe what happens to both lines.

What is the recommended minimum weight for someone 70 inches tall?

Does 𝑊 represent a one-to-one function? Explain your reasoning.

The table below represents a function C that computes the percentage of the time that the sky is cloudy in Augusta, Georgia, where x corresponds to the standard numbers for the months.Construct a table of the inverse of this relationship.

Determine if the inverse of C(x) is a function. Justify your response.

Is the following graph one-to-one?

Does the following graph have an inverse that is a function?

From the video, what is an inverse function?

The video makes finding an inverse function look so easy. What is step 1 to finding an inverse function?

From the video, what is step 2 to finding an inverse function?

From the video, what is step 3 to finding an inverse function?

Check all the options to the right to make it work.What happens as the slope (m) increases? Describe what happens to both lines.

Check all the options to the right to make it work.What happens as the y-intercept (b) increase? Describe what happens to both lines.

What is the recommended minimum weight for someone 70 inches tall?

Does 𝑊 represent a one-to-one function? Explain your reasoning.

What does the inverse compute?

The table below represents a function C that computes the percentage of the time that the sky is cloudy in Augusta, Georgia, where x corresponds to the standard numbers for the months.Construct a table of the inverse of this relationship.

Determine if the inverse of C(x) is a function. Justify your response.

Using a graphing calculator, graph w(k). Choose an appropriate window to view the graph of the function. Does the graph of w(k) pass the Vertical Line Test?

The ideal adult weight for a golden retriever is about 30 kg. How many calories a day should you feed a golden retriever to achieve this ideal weight? Show how you got your answer.

The ideal adult weight for a Schnauzer is about 9 kg. How many calories a day should you feed a Schnauzer to achieve this ideal weight? Show how you got your answer.

Write an equation 𝑘(𝑤) that outputs the number of calories you should feed a dog whose ideal weight is w kg.

Using a graphing calculator, graph k(w). Does the graph of k(w) pass the Vertical Line Test?

Is the following graph one-to-one?

Does the following graph have an inverse that is a function?

Is the following graph one-to-one?

Does the following graph have an inverse that is a function?

What does the inverse compute?

Using a graphing calculator, graph w(k). Choose an appropriate window to view the graph of the function. Does the graph of w(k) pass the Vertical Line Test?

The ideal adult weight for a golden retriever is about 30 kg. How many calories a day should you feed a golden retriever to achieve this ideal weight? Show how you got your answer.

The ideal adult weight for a Schnauzer is about 9 kg. How many calories a day should you feed a Schnauzer to achieve this ideal weight? Show how you got your answer.

Write an equation 𝑘(𝑤) that outputs the number of calories you should feed a dog whose ideal weight is w kg.

Using a graphing calculator, graph k(w). Does the graph of k(w) pass the Vertical Line Test?

Is the following graph one-to-one?

Does the following graph have an inverse that is a function?

The video makes finding an inverse function look so easy.
What is step 1 to finding an inverse function?

Check all the options to the right to make it work.
What happens as the slope (m) increases? Describe what happens to both lines.

Check all the options to the right to make it work.
What happens as the y-intercept (b) increase? Describe what happens to both lines.

The table below represents a function C that computes the percentage of the time that the sky is cloudy in Augusta, Georgia, where x corresponds to the standard numbers for the months.
Construct a table of the inverse of this relationship.

The video makes finding an inverse function look so easy.
What is step 1 to finding an inverse function?

Check all the options to the right to make it work.
What happens as the slope (m) increases? Describe what happens to both lines.

Check all the options to the right to make it work.
What happens as the y-intercept (b) increase? Describe what happens to both lines.

The table below represents a function C that computes the percentage of the time that the sky is cloudy in Augusta, Georgia, where x corresponds to the standard numbers for the months.
Construct a table of the inverse of this relationship.