Precalculus, Unit 3: Exponential and Logarithmic Functions. Key terms, formulas, and worked-example cues a high school student meets for this unit, building on prior units. Front: the term, formula name, or short problem cue. Back: the definition, formula, or solution method.
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- What is an exponential function's general form?
- f(x) = a times b^x
- What does the base of an exponential function determine?
- Whether it models growth (b>1) or decay (0<b<1)
- What is the natural exponential function?
- f(x) = e^x, where e is approximately 2.718
- What is a logarithmic function?
- The inverse of an exponential function, f(x) = log_b(x)
- What is the relationship between exponential and logarithmic functions?
- They are inverse functions of each other
- What is the domain of f(x) = log_b(x)?
- x > 0
- What is the range of f(x) = b^x?
- y > 0
- What is the horizontal asymptote of a basic exponential function?
- y = 0
- What is the vertical asymptote of a basic logarithmic function?
- x = 0
- What is the product rule of logarithms?
- log_b(MN) = log_b(M) + log_b(N)
- What is the quotient rule of logarithms?
- log_b(M/N) = log_b(M) - log_b(N)
- What is the power rule of logarithms?
- log_b(M^p) = p times log_b(M)
- What is the change of base formula?
- log_b(x) = ln(x) / ln(b)
- What does 'ln' represent?
- The natural logarithm, base e
- How do you solve an exponential equation with matching bases?
- Set the exponents equal and solve
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