1. Exponential Equations
Characteristics
Exponential Equations

2. y = abx +k

3. Analyze the function y=2x
a b k-0
Domain is…
All real numbers
Range is …
y>0
Asymptote is …
y=0
Rate of Change is … 2
y - Intercept is … 1

4. Analyze the function y = ½ x
a b- 1/ k- 0
Domain is…
All real numbers
Range is …
y> 0
Asymptote is …
y=0
Rate of Change is …
1/2
y - Intercept is … 1

5. Analyze the function y=3(2)x
a-3 b- 2 k- 0
Domain is…
All real numbers
Range is …
y > 0
Asymptote is …
y = 0
Rate of Change is … 2
y - Intercept is … 3

6. Analyze the function y = 3 (½) x
a- 3 b- ½ k- 0
Domain is…
All real numbers
Range is …
y> 0
Asymptote is …
y = 0
Rate of Change is …
1/2
y - Intercept is … 3

7. Analyze the function y = 3(2)x + 5
a- 3 b-2 k- +5
Domain is…
All real numbers
Range is …
y>8
Asymptote is …
y=8
Rate of Change is … 2
y - Intercept is …
3 + 5 = 8

8. Analyze the function y = 3( ½ )x + 5
a- 3 b- ½ k- +5
Domain is…
All real numbers
Range is …
y>5
Asymptote is …
y=5
Rate of Change is …
1/2
y - Intercept is …
3+5 = 8

9. Analyze the function y = 3(2)x - 5
a- 3 b k- (-5)
Domain is…
All real numbers
Range is …
y> -5
Asymptote is …
y=-5
Rate of Change is … 2
y - Intercept is …
3 + (-5) = -2

10. Analyze the function y = 3( ½ )x - 5
a b-1/2 k- -5
Domain is…
All real numbers
Range is …
y>-5
Asymptote is …
y= -5
Rate of Change is …
1/2
y - Intercept is …
3- (-5)=8

11. Analyze the function y = -3(2)x
a- -3 b- 2 k- 0
Domain is…
All real numbers
Range is …
y< 0
Asymptote is …
y=0
Rate of Change is … 2
y - Intercept is … -3

12. Analyze the function y = -3 ( ½ )x
a- -3 b-1/2 k-0
Domain is…
All real numbers
Range is …
y<0
Asymptote is …
y=0
Rate of Change is …
1/2
y - Intercept is … -3

13. Analyze the function y = -3 ( ½ )x +1
a b- 2 k- +1
Domain is…
All real numbers
Range is …
y<+1
Asymptote is … 1
Rate of Change is … 2
y - Intercept is …
-3+1 = -2

14. Analyze the function y = -3 ( 2 )x - 1
a= -3 b=2 k= -1
Domain is…
All Real Numbers
Range is …
y< -1
Asymptote is …
y=-1
Rate of Change is … 2
y - Intercept is …
-3-1=-4

15. Analyze the function y = -3 ( ½ )x -1
A= -3 b= 1/2 k= -1
Domain is…
All real numbers
Range is …
y< -1
Asymptote is … -1
Rate of Change is …
1/2
y - Intercept is …
-3-1 = -4

16. Find the a y-intercept = a + k Find k Find the y-intercept Find a 2 3

17. Find the a y-intercept = a + k Find k Find the y-intercept Find a -4-3
Find a
-3 = a+ -4
1 = a

18. Find a y-intercept = a + k Find k Find the y-intercept Find a -4 -2