Use the graphing calculator to graph these functions: y1= 2x ; y2= 2x2 ; y3 = 2x after what y-value does the exponential function appear to surpass the linear function? 4 after approximately what y-value does the exponential function surpass the quadratic function?

Using a graphing calculator or a plotting tool for each of the equations, we proceed to answer your problem.

Please see attached graph

1. After what y-value does the exponential function appear to surpass the linear function?

The exponential function surpasses the linear function in

x ∈ (-∞, 1) ∪  (2,∞)

After y = 4 the exponential function definitely surpasses the linear function.  

2.After approximately what y-value does the exponential function surpass the quadratic function?

(See second picture attached)

After y = 79.878 the exponential function surpasses the quadratic function.  

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step-by-step explanation:

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substitute,

circle 1 = 5

circle 2 = 20

circle 3 = 44

in this case no matter how you add, you will always get a perfect square..

hence proved

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