MHF UI Unit Da Graphing Eponential Functions. Using a table of values (no decimals), graph the function.. For the function, state: a) domain b) range c) equation of the asmptote d) -intercept e) -intercept f) increasing or decreasing function? g) end behaviours as, f as f 0 - - -, 0 9 7 0 9 7 - - - - -. Using a table of values (no decimals), graph the functions and on grid above. 0 - - - 0 - - -. Discuss the similarities between the functions, and.. Where would the graph of the function be located?. Where would the graph of the function 0 be located?
MHF UI Unit Da 7. Using a table of values (no decimals), graph the function on the same grid as. 0 - - -. For the function, state: a) domain b) range c) equation of the asmptote d) -intercept e) -intercept f) increasing or decreasing function? g) end behaviours as, f as f, 9. Discuss the similarities between the functions and. 0. Discuss the differences between the functions and.. How is the graph of related to the graph of?. What point is common to all of these eponential functions? Wh?
MHF UI Unit Da Solving Eponential Equations Eponential equations have the unknown () in the eponent. Steps for solving:. Isolate the power with the unknown. Epress the L.S. and R.S. as powers with the same base.. Set the eponents equal.. Solve for the unknown.. Solve for. a) 9-7 0 b) 7 9 c) - d) Check for c)
MHF UI Unit Da Transformations of Eponential Functions. For each function, describe the transformations and graph. a) b) Base Function: Transformations: Transformation: Locate points from new origin : Locate points from new origin : 0 0 0 0 - - - - - - - - - - - - - - - - - - -0-0 - - - - - - - - -0-0
MHF UI Unit Da c) d) Transformation: Transformations: Locate points from new origin : Locate points from new origin : 0 0 0 0 - - - - - - - - - - - - - - - - - - -0-0 - - - - - - - - -0-0
MHF UI Unit Da. For each function, describe the transformations, graph and state the domain and range. a) Base Function: Transformations: b) Base Function: Transformations: Locate points from new origin : Locate points from new origin : Domain: Range: Domain: Range: 0 0 0 0 - - - - - - - - - - - - - - - - - - -0-0 - - - - - - - - -0-0
MHF UI Unit Da Graphing Logarithmic Functions. Using a table of values (no decimals), graph the function on the grid below.. Graph the inverse of on the same grid. 0 - - - 0 0 - - - 0 0 - - -. For log, state: a) domain b) range c) equation of the asmptote d) -intercept e) -intercept f) increasing or decreasing function? g) end behaviour as,f(),f()
MHF UI Unit Da. Using a table of values (no decimals), graph the function on the grid below. 0 - - -. Graph the inverse of on the same grid. 0 0 - - - 0 0 - -. For log, state: a) domain b) range - c) equation of the asmptote d) -intercept e) -intercept f) increasing or decreasing function? g) end behaviour as,f(),f()
MHF UI Unit Da Evaluating Logarithms. Complete the following table. Logarithmic Form log log 9 log Eponential Form 0 log N e b. Evaluate. a) log b) log c) log d) 9 log e) 9 log 0 000 f) log g) log 7 h) log 00 i) 7 log 7 j) log k) log l) log m) 7 log 7 9 n) log 0 Properties of the Logarithmic Function
MHF UI Unit Da Transformations of Logarithmic Functions. Graph the following base logarithmic functions. a) log Ep.Form - 0 0 0 - - - - - b) log Ep.Form - 0 0 0 - - - - - c) log Ep.Form - 0 0 0 - - - - -
MHF UI Unit Da. Given the base function log and the following equations, state the transformations on the base function and graph the transformed equation. log Locate points from new Transformations origin : Base Function Ep. Form - 0 0 0 - - - - - log Locate points from new origin : Transformations Base Function Ep. Form - - -0 - - - - 0 - - - - - log Locate points from new origin : Transformations Base Function Ep. Form - - -0 - - - - 0 - - - - -
MHF UI Unit Da. For each function, describe the transformations, graph and state the domain and range. a) log Base Function: Ep. Form: Transformations: b) log Base Function: Ep. Form: Transformations: Locate points from new origin : Locate points from new origin : Domain: Range: Increasing/decreasing function? End behaviours 0 9 7 Domain: Range: Increasing/decreasing function? End behaviours 0 9 7 - - 0 - - - - - - -7 - -9-0 - - -0 - - - - - - - - - - -7 - -9-0
MHF UI Unit Da Laws of Logarithms Evaluate each of the following, without a calculator: log log log log 7 log log log log log log log log 9 Notice an patterns for each row? Product Law Proof of the product law:
MHF UI Unit Da Evaluate each of the following, without a calculator: log log log log 9 log log log log 9 log log log log Notice an patterns for each row? Quotient Law Proof of the quotient law:
MHF UI Unit Da Etension: Powers Law Proof of the powers law:. Evaluate without a calculator. a) log log b) log 00 -log c) log log log d) e) log log 0 f) log 9 g) log9 log
MHF UI Unit Da. Evaluate log, accurate to decimal places.
MHF UI Unit Da Laws of Logarithms Evaluate each of the following, without a calculator: log log log log 7 log log log log log log log log 9 log log log log 9 log log log log 9 log log log log
MHF UI Unit Da Change of Base Formula Recall: Evaluate log, accurate to decimal places. B observation, if we substitute the letters a, M then: This can be etended to: Proof: Evaluate log, accurate to decimal places.
MHF UI Unit Da Solving Eponential Equations b Factoring. Solve for. a) - 000 b) 7-7 - c) 90
MHF UI Unit Da 7 Solving Eponential Equations Using Logarithms. Solve for. State an eact answer using base 0. Also state an approimate answer accurate to decimal places. b) Method : Method : b) Method : Method :
MHF UI Unit Da 7 c) (7 - ) Method : Method : d) 7 - Method : Method :
MHF UI Unit Da Solving Logarithmic Equations. Evaluate. c) log 0 b) log (-) Note: Compare to Grade.. Solve, stating necessar restrictions. a) log b) log log ( )
MHF UI Unit Da c) log ( - ) -log ( ) d) log log log 7 e) log ( ) log ( )
MHF UI Unit Da Evaluating Logarithms. Evaluate a) log Method : Method : b) log 7 Method : Method : c) log 9 7 d) log e) log f) log g) log () h) log