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Graphing exponential functions worksheets

Graph eight exponential functions or write equations from curves with exact marked points. Compare growth, decay and translations on fixed unit grids with separate answer keys.

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For a graph problem, plot exact points and draw a smooth exponential curve approaching its horizontal asymptote. For a write problem, use the two marked points and the model y = a · b^x to determine a and b.

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Plot exact points. Follow growth or decay.

Each worksheet has eight tasks. Choose graphing, writing equations, or mixed practice with the first four graphing tasks followed by four writing tasks.

For y = a·b^(x − h) + k, use the horizontal asymptote y = k and plot the exact anchor point at x = h and a second point one unit away. Bases 2, 3 and 4 show growth; bases 1/2, 1/3 and 1/4 show decay.

Writing tasks use y = a·b^x and two exact marked points. The value at x = 0 gives a. To find b, divide the output at the larger x-value by the output one unit before it.

Learning objective

What this activity builds

Connect an exponential equation to its growth or decay curve, horizontal asymptote and exact points.

Worked example

Write the equation for an unshifted exponential curve through (0, 3) and (1, 6).

y = 3 · 2^x.

At x = 0, b^0 = 1, so the y-value gives a = 3. Moving one unit right multiplies the output by 6/3 = 2, so b = 2.

Teaching notes

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  • Identify growth when the curve rises from left to right and decay when it falls.
  • Use x = h to locate the exact value a + k.
  • Draw y = k as a horizontal asymptote for a translated graph.
  • Keep the curve above its asymptote because a is positive.
  • For a write problem, the point at x = 0 gives the amplitude directly.
  • Use the ratio of consecutive outputs to determine the base.

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Math SheetNameScore/ 8TeacherDateGraphing Exponential FunctionsGraph the first four exponential functions. For the last four, use the curve and marked points to write y = a · b^x.1. y =5·13x+2+3-10-5510-305101517xy2. y =3·3x-10-5510-305101517xy3. y =4·12x-10-5510-305101517xy4. y =3·2x+2-10-5510-305101517xymath-sheet.comPage 1 / 2
Math SheetNameScore/ 8TeacherDateGraphing Exponential FunctionsGraph the first four exponential functions. For the last four, use the curve and marked points to write y = a · b^x.5. Write y = a · b^x.-10-5510-305101517xyPoints: (0, 5) and (-1, 5/4)Equation: __________________________________6. Write y = a · b^x.-10-5510-305101517xyPoints: (0, 3) and (1, 1)Equation: __________________________________7. Write y = a · b^x.-10-5510-305101517xyPoints: (0, 5) and (-1, 5/3)Equation: __________________________________8. Write y = a · b^x.-10-5510-305101517xyPoints: (0, 5) and (1, 5/4)Equation: __________________________________math-sheet.comPage 2 / 2

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