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Exponential Functions quiz

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  • What is the main difference between a polynomial function and an exponential function?
    A polynomial function has a variable base and a constant exponent, while an exponential function has a constant base and a variable exponent.
  • What are the three requirements for the base of an exponential function?
    The base must be constant, positive, and not equal to 1.
  • In the function f(x) = 2^x, what is the base and what is the power?
    The base is 2 and the power is x.
  • Is f(y) = 1^y an exponential function? Why or why not?
    No, because the base is 1, which does not meet the requirement that the base cannot be 1.
  • Can the base of an exponential function be a fraction? Give an example.
    Yes, as long as it is constant and positive, such as f(x) = (2/3)^x.
  • How do you evaluate f(x) = 2^x for x = 4?
    Substitute 4 for x to get 2^4, which equals 16.
  • What does a negative exponent in an exponential function indicate?
    A negative exponent means you take the reciprocal of the base raised to the positive exponent.
  • Evaluate f(x) = 2^x for x = -3.
    2^-3 equals 1/(2^3), which is 1/8.
  • How would you evaluate f(x) = 2^x for x = 3.14?
    Use a calculator to compute 2^3.14, which is approximately 8.815.
  • Why might you use a calculator when evaluating exponential functions?
    Calculators are helpful for non-integer or large exponents that are difficult to compute by hand.
  • What is the value of f(x) = 2^x when x = 12?
    2^12 equals 4,096.
  • In the function f(x) = 10^(x+1), what is the base and what is the power?
    The base is 10 and the power is (x+1).
  • What distinguishes an exponential function from a function like f(x) = x^2?
    An exponential function has a constant base and a variable exponent, while f(x) = x^2 has a variable base and a constant exponent.
  • What key do you use on a calculator to enter an exponent?
    You use the caret key (^) to enter an exponent on a calculator.
  • If f(x) = 2^x, what is f(0)?
    f(0) = 2^0, which equals 1.