Answer:
4.[tex]g(x)=(1.5)^x-4[/tex]
Step-by-step explanation:
We are given that a graph of the function in the figure.
The equation of parent function
[tex]f(x)=1.5^x[/tex]
We have to find the equation of graph of the function shown in the figure.
The given graph cuts the y- axis at point (0,-3).
The given graph passing through the point (2,-1.75).
1.[tex]g(x)=1.5^x-2[/tex]
Substitute x=0
[tex]g(0)=(1.5)^0-2=1-2=-1[/tex]
The graph cut the y- axis at the point (0,-1).
Therefore, it is not an equation given graph.
2.[tex]g(x)=(1.5)^x-3[/tex]
Substitute x=0
[tex]g(0)=(1.5)^0-3=1-3=-2[/tex]
The graph cut the y- axis at the point (0,-2).
Therefore, it is not an equation given graph.
3.[tex]g(x)=(1.5)^x+2[/tex]
Substitute x=0
[tex]g(0)=(1.5)^0+2=1+2=3[/tex]
The graph cut the y- axis at the point (0,3).
Therefore, it is not an equation given graph.
4.[tex]g(x)=(1.5)^x-4[/tex]
Substitute x=0
[tex]g(0)=(1.5)^0-4=1-4=-3[/tex]
The graph cut the y- axis at the point (0,-3).
Substitute x=2
[tex]g(2)=(1.5)^2-4=-1.75[/tex]
The graph passing through the point (2,-1.75).
Hence, it is an equation of given graph.
