Answer:
Part 1) [tex]g(x)=\frac{2}{5}^{x}[/tex] ----> y-intercept at (0,1)
The graph initially decreases rapidly and then decreases slowly
Part 2) [tex]d(x)=5(\frac{2}{5})^{x}[/tex] ----> y-intercept at (0,5)
The graph initially decreases rapidly and then decreases slowly
Part 3) [tex]h(x)=4^{x}[/tex] ----> y-intercept at (0,1)
The graph initially increases slowly and then increases rapidly
Step-by-step explanation:
we know that
The y-intercept is the value of y when the value of x is equal to zero
Part 1) we have
[tex]g(x)=\frac{2}{5}^{x}[/tex]
Find the y-intercept
For x=0
[tex]g(0)=\frac{2}{5}^{0}=1[/tex]
The y-intercept is the point (0,1)
using a graphing tool
see the attached figure N 1
therefore
y-intercept at (0,1)
The graph initially decreases rapidly and then decreases slowly
Part 2) we have
[tex]d(x)=5(\frac{2}{5})^{x}[/tex]
Find the y-intercept
For x=0
[tex]d(0)=5(\frac{2}{5})^{0}[/tex]
[tex]d(0)=5(1)=5[/tex]
The y-intercept is the point (0,5)
using a graphing tool
see the attached figure N 2
therefore
y-intercept at (0,5)
The graph initially decreases rapidly and then decreases slowly
Part 3) we have
[tex]h(x)=4^{x}[/tex]
Find the y-intercept
For x=0
[tex]h(0)=4^{0}=1[/tex]
The y-intercept is the point (0,1)
using a graphing tool
see the attached figure N 3
therefore
y-intercept at (0,1)
The graph initially increases slowly and then increases rapidly
