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Delta y formula worksheets

Find the symbolic change in y for polynomial, rational, composite and trigonometric functions.

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Find Delta y = f(x + Delta x) - f(x) and preserve the domain at both arguments.

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Practice with exact answers

Keep fractions, radicals and pi exact. Round only when a question asks for a decimal answer, and check every original domain restriction.

Learning objective

What this activity builds

Substitute x + Delta x and subtract the original function without forming a quotient.

Worked example

How does a rate arise from a function?

Compare function values, then divide by the matching input change when the task asks for a rate.

Delta y, average rate, a derivative limit and an instantaneous rate are related but distinct quantities. Read the requested form before calculating.

Teaching notes

Make the practice count

  • Keep exact values through the final step.
  • Retain every original domain restriction.
  • Treat trigonometric inputs as radians.
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Math SheetFormula for Delta yFind Delta y = f(x + Delta x) - f(x).1.f(x) = 4sin(-6x+3)2.f(x) = (x^2+1)/(x-2)3.f(x) = (x^2-6x)/(2x^2-12x+18)4.f(x) = -2cos(3x-12)5.f(x) = 1(3x^2+1)^56.f(x) = 1(-x^3-x)^-3math-sheet.comPage 1 of 2
Math SheetFormula for Delta yFind Delta y = f(x + Delta x) - f(x).7.f(x) = (1/2)/(x^2-4x+4)+(-3)/(x^2)8.f(x) = 2x^3-x+49.f(x) = x^4-2x^2+310.f(x) = -x^2-3x-5math-sheet.comPage 2 of 2

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