DAY 97 EXPONENTIAL FUNCTIONS: DOMAIN & RANGE
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1 DAY 97 EXPONENTIAL FUNCTIONS: DOMAIN & RANGE
2 EXAMPLE Part I Using a graphing calculator, graph the function and sketch the graph on the grid provided below.
3 EXAMPLE Part I Using a graphing calculator, graph the function and sketch the graph on the grid provided below.
4 1. Is the graph an increasing or decreasing function? Eplain your answer. 2. Trace or use the table feature on your calculator to fill out the tables below. As the value of gets very large, what happens to the value of 2? y
5 1. Is the graph an increasing or decreasing function? Eplain your answer. Increasing function as increases, y increases 2. Trace or use the table feature on your calculator to fill out the tables below. As the value of gets very large, what happens to the value of 2?
6 As the value of gets very small, what happens to the value of 2? y
7 As the value of gets very small, what happens to the value of 2?
8 3. Will the value of 2 ever equal 0? Eplain your answer. 4. Are there any values of that would make 2 undefined? Eplain your answer 5. State the domain and range for f ( ) 2 Domain: Range:
9 3. Will the value of 2 ever equal 0? Eplain your answer. approaches 0 4. Are there any values of that would make 2 undefined? Eplain your answer no. 5. State the domain and range for f ( ) 2 Domain: R Range: y > 0
10 Part II Using a graphing calculator, graph the function f ( ) 3 f ( ) 2 along with the graph of from Part I, and sketch the graph of on the grid provided below
11 Part II Using a graphing calculator, graph the function f ( ) 3 f ( ) 2 along with the graph of from Part I, and sketch the graph of on the grid provided below
12 1.Is the graph an increasing or decreasing function? Eplain your answer increasing function as increases y increases 2. As the value of gets very large, what happens to the value of 3? also gets large 3. As the value of gets very small, what happens to the value of 3? 3 gets very small 4. How does the graph of compare to the graph of? 3 increases faster that 2
13 f ( ) a 5. a. Given the general form (where a > 1), what effect does increasing the value of "a" have upon the graph? b. What effect does decreasing the value of "a" have upon the graph?
14 f ( ) a 5. a. Given the general form (where a > 1), what effect does increasing the value of "a" have upon the graph? The larger the a, the faster the graph will rise b. What effect does decreasing the value of "a" have upon the graph?
15 Part III Use a graphing calculator to graph the function f ( ) (0.5 ) along with the graph of f ( ) 2 from Part I, and sketch the graph of f ( ) (0.5 ) on the grid provided below.
16 Part III Use a graphing calculator to graph the function f ( ) (0.5 ) along with the graph of f ( ) 2 from Part I, and sketch the graph of f ( ) (0.5 ) on the grid provided below.
17 1. Is the graph an increasing or decreasing function? Eplain your answer. 2. Trace or use the table feature on your calculator to fill out the tables below. As the value of gets very large, what happens to the value of (0.5)? (0.5)
18 1. Is the graph an increasing or decreasing function? Eplain your answer. Decreasing, as increases y decreases 2. Trace or use the table feature on your calculator to fill out the tables below. As the value of gets very large, what happens to the value of (0.5)? (0.5)
19 As the value of gets very small, what happens to the value of (0.5)? (0.5) 3. Will the value of (0.5) ever equal 0? Eplain your answer.
20 As the value of gets very small, what happens to the value of (0.5)? (0.5) Will the value of (0.5) ever equal 0? Eplain your answer. no, it will get very close, but never reach 0.
21 4. Are there any values of that would make (0.5) undefined? Eplain your answer. 5. State the domain and range for Domain: Range:
22 4. Are there any values of that would make (0.5) undefined? Eplain your answer. no, we are never dividing by State the domain and range for Domain: R Range: y > 0
23 6. How does the graph of f ( ) (0.5 ) compare to the graph of? f ( ) 2
24 6. How does the graph of f ( ) (0.5 ) compare to the graph of? f ( ) 2 The graphs are reflected over the y-ais
25 Part IV Use the graphing calculator to graph the function f ( ) (0.8 ) along with the graph of Part III, and sketch the graph of the grid provided below. f ( ) (0.5 ) f ( ) (0.8 ) from on
26 Part IV Use the graphing calculator to graph the function f ( ) (0.8 ) along with the graph of Part III, and sketch the graph of the grid provided below. f ( ) (0.5 ) f ( ) (0.8 ) from on
27 1. Is the graph an increasing or decreasing function? Eplain your answer. 2. As the value of gets very large, what happens to the value of (0.8)? 3. As the value of gets very small, what happens to the value of (0.8)?
28 1. Is the graph an increasing or decreasing function? Eplain your answer. Decreasing, as increases y decreases 2. As the value of gets very large, what happens to the value of (0.8)? (0.5) gets smaller 3. As the value of gets very small, what happens to the value of (0.8)? (0.5) gets larger
29 f ( ) (0.8 ) 4. How does the graph of compare to the graph of? f ( ) (0.5 ) f ( ) a 5. a. Given the general form (where 0 < a < 1), what effect does increasing the value of "a" have upon the graph? b. What effect does decreasing the value of "a" have upon the graph?
30 f ( ) (0.8 ) 4. How does the graph of compare to the graph of? f ( ) (0.5 ) The graph (0.8) decreases slower that (0.5) f ( ) a 5. a. Given the general form (where 0 < a < 1), what effect does increasing the value of "a" have upon the graph? The higher the value or a closer a gets to 1, the more the graph will look like horizontal line where y=1 b. What effect does decreasing the value of "a" have upon the graph?
31 EXAMPLE Sketch the graph of and range. g( ) 2 1. State the domain The graph of this function is a vertical translation of the graph f()=2 down one unit. f() = 2 f() = 2-1 Domain: (, ) Range: ( 1, ) y = 1
32 EXAMPLE Sketch the graph of and range. g( ) 2. State the domain The graph of this function is a reflection the graph f()=2 in the y-ais. f() = 2 - f() = 2 Domain: (, ) Range: (0, )
33
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