The question requires us to explain the different exponential graphs:
Exponential functions are given by:
f(x)=a(b)^x
when:
a is negative, the graph will be reflected along y-axis
b>1 the graph will be an exponential growth
b<1 the graph will be an exponential decay
1] a]
y=3(2)^x
y-intercept:
at y-intercept x=0 thus
y=3(2)^0
y=3(1)=3
thus y intercept is at y=3
c] since there is no asymptote
d] Domain:
All real numbers
e] Range:
[0,∞)
That all positive real numbers.
2]
a] f(x)=2(0.25)^x
a=2
b=0.25
b<1
thus the function is exponential decay
b] The horizontal axis is at y=0.
c] Domain:
The domain is all real numbers.
d] Range:
The range are all positive values.
e] y-intercept
f(x)=2(0.25)^x
at y-intercept , x=0 thus
y=2(0.25)^0
y=2(1)
y=2
3] y=-5(2)^x
a] This is a decay function since a=-5
b] y-intercept
f(x)=-5(2)^x
f(x)=-5(2)^0
f(x)=-5
C] the asymptote is y=0
d] Domain are all real numbers
e] Range
Range are all negative real numbers
