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Introduction to Exponential Functions quiz

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  • What is the main difference between a polynomial function and an exponential function?
    In a polynomial function, the variable is the base, while in an exponential function, the variable is in the exponent.
  • What are the three requirements for the base of an exponential function?
    The base must be a constant, positive, and not equal to 1.
  • What must the exponent of an exponential function contain?
    The exponent must contain a variable.
  • Is f(x) = 2/3^x an exponential function? Why or why not?
    Yes, because the base (2/3) is constant, positive, and not 1, and the exponent contains a variable.
  • 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 equal to 1.
  • Is f(x) = 10^(x+1) an exponential function? Why or why not?
    Yes, because the base (10) is constant, positive, and not 1, and the exponent (x+1) contains a variable.
  • What is the base and exponent in the function f(x) = 2/3^x?
    The base is 2/3 and the exponent is x.
  • What is the base and exponent in the function f(x) = 10^(x+1)?
    The base is 10 and the exponent is x+1.
  • How do you evaluate f(x) = 2^x for x = 4?
    Plug 4 in for x to get 2^4, which equals 16.
  • How do you evaluate f(x) = 2^x for x = -3?
    Plug -3 in for x to get 2^-3, which equals 1/8.
  • How do you evaluate f(x) = 2^x for x = 3.14?
    Plug 3.14 in for x and use a calculator to compute 2^3.14, which is approximately 8.815.
  • How do you evaluate f(x) = 2^x for x = 12?
    Plug 12 in for x and use a calculator to compute 2^12, which equals 4096.
  • What calculator key is used to raise a number to a power?
    The caret (^) key is used to raise a number to a power.
  • Why is it okay for the base of an exponential function to be a fraction?
    It is okay as long as the base is constant and positive.
  • What happens when the exponent in an exponential function is negative?
    A negative exponent means the function value is the reciprocal of the base raised to the positive exponent.