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## Functions and Logarithms

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**Functions and Logarithms**Section 1.5**First, some basic review…**What does the Vertical Line Test tell us? Whether or not the graph of a relation is a function… What does the Horizontal Line Test tell us? Whether or not a relation’s inverse is a function… A function that passes both the VLT and HLT is called: One-to-One**Inverses**• Since each output of a one-to-one function comes from just one input, a one-to-one function can be reversed to send outputs back to the inputs from which they came. • The function defined by reversing a one-to-one function f is the inverse of f. • Composing a function with its inverse in either order sends each output back to the input from which it came.**Inverses**Find and verify that First, solve for x: Interchange x and y: Verification: (in the given domains)**Logarithmic Functions**Switching between exponential and logarithmic form: The key element of this “linking” statement: Logarithms ARE Exponents!!!**Logarithmic Functions**• Logarithms with base e and base 10 are so important in applications that calculators have special keys for them. • They also have their own special notations and names.**Logarithmic Functions**How to “read” logarithmic expressions… “b to what power is x?” “Read” each properly, then evaluate: “2 to what power is 8?” “10 to what power is 1/100?” 5 “e to what power is e ?”**Properties of Logarithms**Change of Base (COB) Formula**Guided Practice**Find a formula for Switch x and y, solve for y:**Guided Practice**Solve the equation algebraically. Support graphically. Does the graph support our analytic answer?**Guided Practice**Solve the equation algebraically. Support graphically. This equation is quadratic in ...**Guided Practice**Solve the equation algebraically. Support graphically. Do both of these answers work? Graphical support?