notes on graphing exponential functions

1. EXPONENTIAL FUNCTIONS
SECTION 7.5 PAGE 424

2. EXPONENTIAL FUNCTION 𝑦 = 𝑎𝑏 𝑥
Variable 𝑥 is in the exponent.
𝑎 ∶ ____________________________________
𝑏 ∶ ____________________________________
𝑏 > 1: ______________________________________
0 < 𝑏 < 1: _________________________________

3. GRAPH 𝑦 = 3 𝑥
𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡: ______________________
𝑔𝑟𝑜𝑤𝑡ℎ 𝑜𝑟 𝑑𝑒𝑐𝑎𝑦 𝑓𝑎𝑐𝑡𝑜𝑟: ______________
X Y
Will the graph ever cross the x-axis?

4. ASYMPTOTE
𝑦 = 𝑎𝑏 𝑥
+ 𝑘

5. GRAPH 𝑦 = 3 𝑥
− 2
𝑔𝑟𝑜𝑤𝑡ℎ 𝑜𝑟 𝑑𝑒𝑐𝑎𝑦 𝑓𝑎𝑐𝑡𝑜𝑟: _______________
𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡: ______________________
𝑎𝑠𝑦𝑚𝑝𝑡𝑜𝑡𝑒: _____________________
X Y

6. GRAPH 𝑦 = 3 ∙
1
2
𝑥
𝑔𝑟𝑜𝑤𝑡ℎ 𝑜𝑟 𝑑𝑒𝑐𝑎𝑦 𝑓𝑎𝑐𝑡𝑜𝑟: ______________
𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡: ______________________
𝑎𝑠𝑦𝑚𝑝𝑡𝑜𝑡𝑒: _____________________
X Y

7. GRAPH 𝑦 = 3 ∙
1
2
𝑥
+ 2
𝑔𝑟𝑜𝑤𝑡ℎ 𝑜𝑟 𝑑𝑒𝑐𝑎𝑦 𝑓𝑎𝑐𝑡𝑜𝑟: ______________
𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡: ______________________
𝑎𝑠𝑦𝑚𝑝𝑡𝑜𝑡𝑒: _____________________
X Y

8. GRAPH 𝑦 = −3 ∙ 2 𝑥
𝑔𝑟𝑜𝑤𝑡ℎ 𝑜𝑟 𝑑𝑒𝑐𝑎𝑦 𝑓𝑎𝑐𝑡𝑜𝑟: _______________
𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡: ______________________
𝑎𝑠𝑦𝑚𝑝𝑡𝑜𝑡𝑒: _____________________
X Y

9. GRAPH 𝑦 = −2 ∙ 3 𝑥
+ 5
𝑔𝑟𝑜𝑤𝑡ℎ 𝑜𝑟 𝑑𝑒𝑐𝑎𝑦 𝑓𝑎𝑐𝑡𝑜𝑟: ______________
𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡: ______________________
𝑎𝑠𝑦𝑚𝑝𝑡𝑜𝑡𝑒: _____________________
X Y

10. GRAPH 𝑦 = −2 ∙
1
3
𝑥
𝑔𝑟𝑜𝑤𝑡ℎ 𝑜𝑟 𝑑𝑒𝑐𝑎𝑦 𝑓𝑎𝑐𝑡𝑜𝑟: ______________
𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡: ______________________
𝑎𝑠𝑦𝑚𝑝𝑡𝑜𝑡𝑒: _____________________
X Y

11. GRAPH 𝑦 = −2 ∙
1
3
𝑥
− 2
𝑔𝑟𝑜𝑤𝑡ℎ 𝑜𝑟 𝑑𝑒𝑐𝑎𝑦 𝑓𝑎𝑐𝑡𝑜𝑟: ______________
𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡: ______________________
𝑎𝑠𝑦𝑚𝑝𝑡𝑜𝑡𝑒: _____________________
X Y