Unit 3 Day 10 – Transformations of Logarithmic Functions.

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Presentation transcript:

Unit 3 Day 10 – Transformations of Logarithmic Functions

Warm-Up 3 1.Find the inverse of: 2.Your parents put $50 into a savings account when you were born to save up money for college. The savings account gains interest at a rate of 2% annually. Write an explicit function to model this situation. 3. Evaluate:

Warm Up 3 Describe the transformation using words!!

Essential Question (Last one!) How can we use equations to determine the transformation of exponential and logarithmic functions? EQ’s are due on Friday!!! Questions and ANSWERS!

Definitions Domain – The x values! Range – The y values!

Asymptote: is a line that a graph approaches, but does not intersect

Asymptote Exponential functions will always have a horizontal asymptote (y = #) Parent function: Has horizontal asymptote of y = 0 This asymptote changes when the graph is moved up and down.

Asymptote Logarithmic functions will always have a vertical asymptote (x = #) Parent function: Has vertical asymptote of x = 0 This asymptote changes when you move the graph left and right.

X – intercept – Where you cross the x – axis! Y – intercept – Where you cross the y – axis!

Exponential Function – A model to model exponential growth or decay – In the form Logarithmic Function – The inverse of an exponential Function – In the form :

Look at # 1 and # 2

Transformations of Logarithmic Functions Parent Functiony = log b x Shift upy = log b x + k Shift downy = log b x - k Shift lefty = log b (x + h) Shift righty = log b (x - h) Combination Shifty = log b (x ± h) ± k Reflect over the x-axisy = -log b x Stretch verticallyy = a log b x Stretch horizontallyy = log b ax

Translations of logarithmic functions are very similar to those for other functions. Describe each translation for parent function y = log x. 1.y = log (x + 2) 2.y = log (x) – 3 3.y = 5 log x 4.y = -log x 5.y = log (x – 4) Left 2 2.Down 3 3.Vertical stretch by 5 4.Reflect over x-axis 5.Right 4, up 5

Identify the asymptote 1.y = log (x + 2) 2.y = log (x) – 3 3.y = 5 log x 4.y = -log x 5.y = log (x – 4) Left 2 so x = x = 0 3.X=0 4.X=0 5.Right 4, so x = 4

Translations of exponential functions are very similar to those for other functions. Describe each translation for parent function Vertical stretch of 2 2. Left 3 3. Down 1 4. Right 6 and down 4 5. Reflect over x-axis, vertical compression of ½, up 5

Translations of exponential functions are very similar to those for other functions. Describe each translation for parent function Y = 0 2. Y = 0 3. Down 1 so y = down 4 so y = -4 5.up 5 so y = 5

Graph the following function on the graph at right. Describe each transformation, give the domain and range, and identify any asymptotes. y = -2log (x + 2) – 4 Domain: Range: Asymptote: Description of transformations:

Guided Practice

Homework Independent Practice with Logarithmic Functions