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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 as the 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.
  • Why is f(y) = 1^y not considered an exponential function?
    Because the base is 1, which does not meet the requirement that the base cannot be equal to 1.
  • In the function f(x) = 2/3^x, what is the base and what is the power?
    The base is 2/3 and the power is x.
  • How do you evaluate an exponential function for a given value of x?
    Substitute the value for x into the exponent and calculate the result using exponent rules.
  • 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.
  • How would you evaluate f(x) = 2^x for x = -3?
    You calculate 2^-3, which equals 1/(2^3) or 1/8.
  • Why might you use a calculator when evaluating exponential functions?
    You use a calculator for non-integer or large exponents that are difficult to compute by hand.
  • What key on a calculator is typically used to enter exponents?
    The caret key (^) is used to raise a number to a power.
  • If f(x) = 2^x, what is f(4)?
    f(4) is 2^4, which equals 16.
  • If f(x) = 2^x, what is f(3.14) approximately?
    f(3.14) is approximately 8.815 when calculated with a calculator.
  • If f(x) = 2^x, what is f(12)?
    f(12) is 2^12, which equals 4096.
  • Can the base of an exponential function be a fraction?
    Yes, as long as the fraction is constant, positive, and not equal to 1.
  • In the function f(x) = 10^(x+1), what is the power?
    The power is x+1.
  • What distinguishes exponential growth or decay from polynomial growth?
    Exponential functions grow or decay much faster because the variable is in headlines the exponent, not the base.