Given:
g(x) vertical shift of [tex]f(x)=-x[/tex] up 3 units followed by a vertical stretch by a factor of 4.
To find:
The rule for g(x).
Solution:
We have,
[tex]f(x)=-x[/tex]
This function shifts 3 units up. So,
[tex]f(x)+3=-x+3[/tex]
This function vertical stretch by a factor of 4. So,
[tex]g(x)=4(f(x)+3)[/tex]
[tex]g(x)=4(-x+3)[/tex]
[tex]g(x)=-4x+12[/tex]
Therefore, the rule for g(x) is [tex]g(x)=-4x+12[/tex].
