IM Alg1.5.20 Lesson: Changes over Equal Intervals

For each given expression, write an equivalent expression with as few terms as possible.
[math]7p-3+2\left(p+1\right)[/math]
[math]\left[4\left(n+1\right)+10\right]-4\left(n+1\right)[/math]
[math]9^5\cdot9^2\cdot9^x[/math]
[math]\frac{2^{4n}}{2^n}[/math]
[left][size=150]Here is a graph of [math]y=f(x)[/math] where [math]f(x)=2x+5[/math].[/size][br][img]data:image/png;base64,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[/img][/left]How do the values of [math]f[/math] change whenever [math]x[/math] increases by 1, for instance, when it increases from 1 to 2, or from 19 to 20? Be prepared to explain or show how you know.
[size=150]Here is an expression we can use to find the difference in the values of [math]f[/math] when the input changes from [math]x[/math] to [math]x+1[/math].[/size][br][br][math]\left[2\left(x+1\right)+5\right]-\left[2x+5\right][/math][br][br]Does this expression have the same value as what you found in the previous questions? Show your reasoning.
How do the values of [math]f[/math] change whenever [math]x[/math] increases by 4? Explain or show how you know.[br]
Write an expression that shows the change in the values of [math]f[/math] when the input value changes from [math]x[/math] to [math]x+4[/math].[br]
Show or explain how that expression has a value of 8.[br]
[size=150]Here is a table that shows some input and output values of an exponential function [math]g[/math]. The equation [math]g\left(x\right)=3^x[/math] defines the function.[/size][br][br]How does [math]g\left(x\right)[/math] change every time [math]x[/math] increases by 1? Show or explain your reasoning.
Choose two new input values that are consecutive whole numbers and find their output values. Record them in the table.[br][br]How do the output values change for those two input values?[br]
Complete the table with the output when the input is x and when it is x+1.[br][br]Look at the change in output values as the [math]x[/math] increases by 1. Does it still agree with your findings earlier? Show your reasoning.
[i]Pause here for a class discussion.[/i] Then, work with your group on the next few questions.[br][br]Choose two [math]x[/math]-values where one is 3 more than the other (for example, 1 and 4). How do the output values of [math]g[/math] change as [math]x[/math] increases by 3? (Each group member should choose a different pair of numbers and study the outputs.)[br]
Complete this table with the output when the input is x and when it is x+3.
Look at the change in output values as [math]x[/math] increases by 3. Does it agree with your group's findings in the previous question? Show your reasoning.
[size=150]For integer inputs, we can think of multiplication as repeated addition and exponentiation as repeated multiplication: [br][br][math]\large{3\cdot 5=3+3+3+3+3\qquad\qquad\qquad\text{ and }\qquad\qquad\qquad 3^5=3\cdot 3\cdot 3\cdot 3\cdot 3}[/math][br][/size][br][size=150]We could continue this process with a new operation called tetration. It uses the symbol [math]\uparrow\uparrow[/math], and is defined as repeated exponentiation:[/size][br][math]3\uparrow\uparrow5=3^{3^{3^{3^3}}}[/math].[br][br]Compute [math]2\uparrow\uparrow3[/math] and [math]3\uparrow\uparrow2[/math].
If [math]f\left(x\right)=3\uparrow\uparrow x[/math], what is the relationship between [math]f\left(x\right)[/math] and [math]f\left(x+1\right)[/math]?

IM Alg1.5.20 Practice: Changes over Equal Intervals

Whenever the input of a function f increases by 1, the output increases by 5.
Which of these equations could define [math]f[/math]?
[size=150]The function [math]f[/math] is defined by [math]f\left(x\right)=2^x[/math]. [/size][br][br]Which of the following statements is true about the values of [math]f[/math]? Select [b]all[/b] that apply. 
The two lines on the coordinate plane are graphs of functions f and g.
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[/img][/center][br]Use the graph to explain why the value of [math]f[/math] increases by 2 each time the input [math]x[/math] increases by 1. 
Use the graph to explain why the value of [math]g[/math] increases by 2 each time the input [math]x[/math] increases by 1.
[size=150]The function [math]h[/math] is given by [math]h\left(x\right)=5^x[/math].[/size][br][br]Find the quotient [math]\frac{h\left(x+2\right)}{h\left(x\right)}[/math].
What does this tell you about how the value of [math]h[/math] changes when the input is increased by 2?
Find the quotient [math]\frac{h\left(x+3\right)}{h\left(x\right)}[/math].
What does this tell you about how the value of [math]h[/math] changes when the input is increased by 3?
For each of the functions [math]f,g,h,p,[/math] and [math]q[/math], the domain is [img]data:image/png;base64,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[/img]. For which functions is the average rate of change a good measure of how the function changes for this domain? Select [b]all [/b]that apply. 
The average price of a gallon of regular gasoline in 2016 was $2.14.
[size=150]In 2017, the average price was $2.42 a gallon—an increase of 13%.[br][/size][br]At that rate, what will the average price of gasoline be in 2020?
A credit card charges a 14% annual nominal interest rate and has a balance of $500.
If no payments are made and interest is compounded quarterly, which expression could be used to calculate the account balance, in dollars, in 3 years?
Here are equations that define four linear functions.
For each function, write a verbal description of what is done to the input to get the output, and then write the inverse function.[br][br][math]a\left(x\right)=x-4[/math]
[math]b\left(x\right)=2x-4[/math]
[math]c\left(x\right)=2\left(x-4\right)[/math]
[math]d\left(x\right)=\frac{x}{4}[/math]

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