Part A
g(x)=f(x)-1
In order to obtain g(x), f(x) was translated 1 unit downwards.
A sketch of the graph is given below.
Part B
h(x)=-f(x)
In order to obtain h(x), f(x) was reflected across the x-axis.
A sketch of h(x) is given below:
Part C
p(x)=f(x+2)
In order to obtain p(x), f(x) was translated left by 2 units.
A sketch of p(x) is given below:
Part D
q(x)=-f(x+2)-1
n order to obtain q(x), f(x) was reflected across the x-axis, translated by 2 units to the left and 1 unit down.
The new points are:
[tex]\begin{gathered} (4,2)\to(4,-2)\to(4-2,-2-1)=(2,-3) \\ (-3,1)\to(-3,-1)\to(-3-2,-1-1)=(-5,-2) \end{gathered}[/tex]
A sketch of q(x) is given below:
