U2D4 Inverse Functions Jan28

Instructions

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6700 dollars is placed in an account with an annual interest rate of 8%. 
How much will be in the account after 24 years, to the nearest cent?

After 24 years there will be $_______  in the account.

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An element with mass 730 grams decays by 27.6% per minute. 
How much of the element is remaining after 12 minutes, to the nearest 10th of a gram?


After 12 minutes there is _______ grams of the element.

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A new car is purchased for 17600 dollars. The value of the car depreciates at 11.75% per year. What will the value of the car be, to the nearest cent, after 11 years?

The value of the car will be $_______  after 11 years.

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From the video, what is an inverse function?

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

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

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

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.

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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?

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

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Find a formula for the inverse.

h = _______ 
Isolate h to get the inverse.

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Evaluate the inverse for 150 pounds and interpret the result.

A person that weighs 150 pounds will be _______  inches tall.

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What does the inverse compute?

Function or Not?

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.

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

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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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?

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If you feed your puppy 800 kcal a day, what is their predicted adult weight? Round to the nearest tenth.

The predicted weight for a puppy eating 800 Kcal a day is _______  kg.

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Complete the table to predict the adult weight of your pet with each of the different diet plans. 
Round to the nearest tenth.

Weight in kg  _______  _______  _______ 

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If you want your dog to weigh 15.6 kg, how many calories should you feed him a day?
A dog that weighs 15.6 kg should eat _______  kcal a day.

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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.

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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.

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

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

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?

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

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Is the following graph one-to-one?

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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?

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.