Have out: Assignment, pencil, red pen, highlighter, GP notebook, graphing calculator U3D3 Bellwork: Solve each of the following for x. 1) 2) 3) 4) +1 +2 +2 +1 +2 +2 total:

Solve Exponential Equations Add to your notes: Solve Exponential Equations Steps: Example #1: 1. Rewrite each base to make a common base. (Refer to your powers worksheet.) 2. By the property of equality, if the bases are equal, then the exponents are equal. 3. Set the exponents equal and solve for x.

Solve Exponential Equations Add to your notes: Solve Exponential Equations Steps: Example #2: 1. Rewrite each base to make a common base. (Refer to your powers worksheet.) 2. By the property of equality, if the bases are equal, then the exponents are equal. 3. Set the exponents equal and solve for x.

Solve Exponential Equations Add to your notes: Solve Exponential Equations Steps: Example #3: 1. Rewrite each base to make a common base. (Refer to your powers worksheet.) 2. By the property of equality, if the bases are equal, then the exponents are equal. 3. Set the exponents equal and solve for x.

Investigating Asymptotes Take out the worksheet: Investigating Asymptotes Determine the following information for the function below, and then graph it. Enter the equation into your graphing calculator in Y= Type into your graphing calculator: ___________. 1) y-intercept: _______

Fill in the values for each table on parts (2), (3), and (5). Recall the steps for getting single values: 2nd QUIT VARS  Y–VARS 1: Function 1: Y1 ( ) Fill in the x–values here Use 2nd ENTER to repeat the steps. 2) What happens as x gets small? 3) What happens as x approaches 3? From the left From the right x y1 x y1 x y1 –0.33 1 –0.5 5 0.5 –1 –0.25 2 –1 4 1 –2 –0.20 2.5 –2 3.5 2 –10 –0.08 2.9 –10 3.1 10 –100 –0.0097 2.99 –100 3.01 100 –1000 –0.000997 2.999 –1000 3.001 1000 y approaches 0. y is more negative. y gets larger.

5) What happens as x gets large? y x 10 –10 x = 3 5) What happens as x gets large? x y1 vertical asymptote 6 0.33 10 0.14 100 0.01 1000 0.001 y gets closer to zero. Plot the points from the tables in parts (2), (3), and (5). undefined 4) When x = 3, the function is _________, so x  3. At x = 3, there is a “invisible” vertical barrier called an __________. asymptote

zero 6) As x gets large or small, y1 approaches _____, but never reaches _____, so we have a __________________ at y = ___. zero horizontal asymptote x = 3 y x 10 –10 7) Domain: ___________ vertical asymptote Range: ____________ horizontal asymptote y = 0

Investigate the given function. Be sure to label each graph. Example #2: Reciprocal function a) Algebraically solve for the y–intercept. b) Algebraically solve for the x–intercepts. This doesn’t make sense. 0 times anything is 0, so 0(x + 3) = 0, not –1. There is no solution. cross multiply Therefore, there are no x–intercepts.

Example #2: Reciprocal function Type f(x) into your calculator, then use to help you graph the function. TABLE y x 10 –10 x = –3 c) Since x  ___, there is a ______________ at x = __. –3 vertical asymptote –3 d) Is there a horizontal asymptote? y = 0 As x  , y  ___ As x  – , y  ___ Therefore, y = ___ is a _________ asymptote. horizontal

Investigate the given function. Be sure to label each graph. Example #3: Reciprocal function a) Algebraically solve for the y–intercept. b) Algebraically solve for the x–intercepts. cross multiply

Example #3: Reciprocal function Type the f(x) into your calculator, then use to help you graph the function. TABLE y x 10 –10 x = –4 c) Since x  ___, there is a ______________ at x = __. –4 vertical asymptote –4 d) Is there a horizontal asymptote? As x  , y  ___ As x  – , y  ___ –2 y = –2 –2 Therefore, y = ___ is a _________ asymptote. –2 horizontal

Complete the worksheet Today’s assignment: Complete the worksheet