Answer:
see attached graphs
Step-by-step explanation:
Transformations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Parent function: [tex]f(x) = x[/tex]
Each transformation is a transformation of the parent function only:
Translation of 4 units down
[tex]\implies f(x)-4=x-4[/tex]
[tex]\implies y=x-4[/tex]
A stretch by a factor of 3
[tex]\implies 3f(x)=3x[/tex]
[tex]\implies y=3x[/tex]
A reflection and a translation 1 unit up
[tex]\implies f(-x)+1=-x+1[/tex]
[tex]\implies y=-x+1[/tex]
