[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]

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]?