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Exponents and radicals practice

Evaluating exponential functions worksheets

Evaluate 14 exponential functions at positive, negative or mixed integer inputs. Keep exact fraction answers and show a hundredth approximation when needed.

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Substitute the stated input and evaluate the function. Keep the exact value; where needed, the key also gives an approximation to the nearest hundredth.

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Keep the exact value before rounding

The key preserves the reduced exact fraction. If its decimal repeats or needs more than two decimal places, it also shows an approximation to the nearest hundredth, with exact halfway cases rounded away from zero.

A negative input changes the power of the base into a reciprocal. It does not make a positive exponential function negative.

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Learning objective

What this activity builds

Substitute an input into f(x) = a·bˣ, evaluate the power first and then multiply by the coefficient.

Worked example

If f(x) = 3 × 2ˣ, what is f(−2)?

3/4.

Replace x with −2. Since 2⁻² = 1/4, multiply 3 by 1/4 to obtain 3/4.

Teaching notes

Make the practice count

  • Write the substitution before calculating.
  • Keep the coefficient outside the power unless parentheses say otherwise.
  • Use negative inputs to connect exponential functions with reciprocals.
  • Round only after finding the exact value.

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Math SheetNameScore/ 14TeacherDateEvaluate Exponential FunctionsSubstitute and keep the exact rational value.1.f(x) =2·1x; f(1)2.f(x) =13·1x; f(-2)3.f(x) =3·23x; f(3)4.f(x) =85·1x; f(-4)5.f(x) =1·35x; f(1)6.f(x) =3·74x; f(-2)7.f(x) =3·1x; f(3)8.f(x) =1·2x; f(-4)9.f(x) =13·53x; f(1)10.f(x) =7·2x; f(-2)math-sheet.comPage 1 / 2
Math SheetNameScore/ 14TeacherDateEvaluate Exponential FunctionsSubstitute and keep the exact rational value.11.f(x) =85·2x; f(3)12.f(x) =74·25x; f(-4)13.f(x) =72·65x; f(1)14.f(x) =32·3x; f(-2)math-sheet.comPage 2 / 2

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