7.2.3 Transforming Exponential and Logarithmic Functions − Worksheet
Example 1: Make a table of values, and graph each function. Describe the asymptote. Tell how the graph is transformed from the graph of f ( x ) = 3 x . 1. g ( x ) = 3 x + 2 2. h ( x ) = 3 x − 2 3. j ( x ) = 3 x + l Example 2: Graph each exponential function. Find the y -intercept and the asymptote. Describe how the graph is transformed from the graph of its parent function. 4. g ( x ) = 3(4 x ) 5. 6. = h x ( ) (4 ) x =− j x ( ) (4 ) x
1 3
1 3
7. k ( x ) = − 2(4 x )
8. m ( x ) = − (4 − x )
9. n ( x ) = e 2 x
Example 3: Graph each logarithmic function. Find the asymptote. Then describe how the graph is transformed from the graph of its parent function. 10. g ( x ) = 2.5log x 11. h ( x ) = 2.5log( x + 3) 12. Example 4: Write each transformed function by using the given parent function and the indicated transformations. 13. The parent exponential function f ( x ) = 0.7 x is horizontally stretched by a factor of 3, reflected across the x -axis, and translated 2 units left. 14. The parent logarithmic function f ( x ) = log x is translated 12 units right, vertically compressed by a factor of 1 2 , and translated 25 units up. Example 5: 15. The height of a poplar tree in feet, at age t years can be modeled by the function h ( t ) = 6 + 3ln( t + l). Describe how the model is transformed from its parent function. Then use the model to predict the number of years when the height will exceed 17 feet. j x x 1 3 ln 1.5 =− + ( )
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