Answer:
1) g(x) ----> y-intercept -3
2) h(x) ----> y-intercept -1
3) f(x) ----> y-intercept 2
Step-by-step explanation:
we know that
The y-intercept or initial value, is the value of y when the value of x is equal to zero
Calculate the y-intercept of each exponential function
case 1) A function g, has a growth factor of 2 and a value of 1, and passes through the point (1,-2)
The exponential function is equal to
[tex]g(x)=1(2)^{x}+c[/tex]
Find the value of c
For x=1, g(x)=-2
substitute
[tex]-2=(2)^{1}+c[/tex]
[tex]-2=2+c[/tex]
[tex]c=-4[/tex]
so
[tex]g(x)=(2)^{x}-4[/tex]
Find the y-intercept
For x=0
[tex]g(0)=(2)^{0}-4[/tex]
[tex]g(0)=-3[/tex]
case 2) Observing the table
For x=0
f(0)=2
therefore
The y-intercept of f(x) is 2
case 3) Observing the graph
For x=0
h(0)=-1
therefore
The y-intercept of h(x) is -1
Order the functions from least to greatest y-intercept
1) g(x) ----> y-intercept -3
2) h(x) ----> y-intercept -1
3) f(x) ----> y-intercept 2
