Answer:
[tex]g(x)=(\frac{1}{4}x)^2[/tex]
Step-by-step explanation:
The given functions are;
[tex]f(x)=x^2[/tex]
The function g(x) is a vertical stretch of f(x) by a factor of 'a' units, therefore we can write g(x) in terms of f(x).
This implies that;
[tex]g(x)=a\bullet f(x)[/tex]
[tex]\implies g(x)=a\bullet x^2[/tex]
The graph of g(x) passes through (4,1).
[tex]\implies g(4)=1[/tex]
[tex]\implies a(4^2)=1[/tex]
[tex]\implies 16a=1[/tex]
[tex]\implies a=\frac{1}{16}[/tex]
This implies that;
[tex]\implies g(x)=\frac{1}{16}x^2[/tex]
Or
[tex]g(x)=(\frac{1}{4}x)^2[/tex]
