Use the approach of Exercise to show thatfor any constant c. [Hint: Compare the tangent li...

Use the approach of Exercise to show that

for any constant c. [Hint: Compare the tangent lines to the graphs of f(x) and f(x) + c.]

Exercise

(a)Draw two graphs of your choice that represent a function y = f(x) and its vertical shift y = f(x) + 3.

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(b)Pick a value of x and consider the points (x, f(x)) and (x, f(x)+3). Draw the tangent lines to the curves at these points and describe what you observe about the tangent lines.

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(c)Based on your observation in part (b), explain why