Presentation on theme: "Bell work Find the value to make the sentence true. NO CALCULATOR!!"— Presentation transcript:
1 Bell work Find the value to make the sentence true. NO CALCULATOR!! 23 = x5x = 25(½)3=xX (1/2) = 5
2 Graph f(x) = 2xName 3 points on f(x)Graph y = xGraph f-1 (x)Write an equation for the inverse.
3 F(x) = 2x to write the equation of the inverse, switch the x and y values x = 2y How do you solve for y? Verbally we would say that “Y is the exponent that 2 to raised to in order to get x.”To write it mathematically: y = log2x
4 A logarithm is just an exponent So the inverse of an exponential function is a logarithmic function. (This means that exponentiation “undoes” logarizing and vice versa.)Definition of logarithm:X = ay can be rewritten as logax = y(a>0, a≠1, x>0)** Why is domain positive? ** What # can be raised to power and give you a negative? **
5 Any exponential expression can be written as a logarithmic expression and vice versa Rewrite in exponential form.log28 = 3log381=4log164 = ½log273 = ⅓
6 Any exponential expression can be written as a logarithmic expression and vice versa Rewrite as a logarithmic expression.52 = 2534 = 81(½)3 = ⅛(2)-2 = ¼
7 Remember: A logarithm is an exponent Evaluate.log216=** Think: 2 to what power gives me 16?**log327= _____log22=_____log101000=____2 log31= _____
8 Common logarithm The common logarithm is a log with base of 10. When the base is 10, we don’t write it!!Example: log 100 = 2 (Understood base 10)The calculator uses the common base of 10 when you plug in a value.Use the calculator to find log 10
9 Natural logarithm The natural logarithm is a log with base e. Abbreviation is lnloge5 will be written as ln 5* “ln” means the base is understood to be e*What is the value of ln e?
10 Some other important properties that always hold true: loga1=0logaa=1logaax=xln1 = 0ln e = 1lnex=x
12 If logax=logay, then x=y Solve for x:log2x=log23Solve for x:log44= x
13 Steps to graphing a logarithmic function Rewrite as an exponential equationPick values for Y and solve for xPlot the points.
14 Graph y = log 2x Rewrite as Exponential equation: ___________ Domain: Range:Intercepts:Asymptotes:How is this related to the graph y =2x?
15 Graph f(x) = log3xRewrite as an exponential equation: ___________________Domain:Range:Intercepts:Asymptotes:
16 Graph y = log 4 xRewrite as an exponential equation: ___________________DomainRangeInterceptsAsymtpotes
17 Graph y = lnx Rewrite as an exponential equation: ___________________ Domain:Range:Intercepts:Asymptotes:
18 Graph y = log3(x-2)Rewrite as an exponential equation: ___________________Domain:Range:Intercepts:Asymptotes:
19 Transformations What happens to the graph of f(x±c)? Moves right or left c unitsWhat happens to the graph of f(x) ± c?Moves the graph up or down c unitsWhat happens to the graph of f(-x)?Reflects across the y axisWhat happens to the graph of –f(x)?Reflects across the x axis
20 Suppose f(x) = log2x Describe the change in the graph G(x) = log2(-x)Reflect over the y axisG(x) = log2 (x+5)Moves 5 units to the left, VA: x = -5G(x) = -log2(x)Reflect over the x axisG(x) = log2x-4Moves the graph down 4 unitsg(x) = log 2 (x-3)Moves the graph 3 units to the right, VA: x = 3
21 Sketch the following graphs Don’t forget RXSRY Y = -lnx2. Y = ln(-x)Y = ln(x-2)Y = lnx + 3