Answer:
(a)
f(x) is shifted left side by 2 units
(b)
f(x) is vertically compress by 2 units
(c)
f(x) is horizontally compress by 4 units
f(x) is vertically shifted upside by 3 units
Step-by-step explanation:
we are given
parent function as
[tex]f(x)=x^3[/tex]
(a)
we have
[tex]g(x)=(x+2)^3[/tex]
we can see that in place x , we have x+2
It means that f(x) is shifted left side by 2 units
So, f(x) is shifted left side by 2 units
(b)
[tex]g(x)=-\frac{1}{2}x^3[/tex]
we can see that -1/2 is multiplied
Since, negative sign is multiplied to y-value
so, f(x) is reflected about x-axis
and 1/2 is multiplied to y-value
so, f(x) is vertically compress by 2 units
(c)
we are given
[tex]g(x)=(4x)^3+3[/tex]
we can see that in place x , we have 4x
so, f(x) is horizontally compress by 4 units
and 3 is added to y-value
so, f(x) is vertically shifted upside by 3 units
