Given that:
Parent equation : [tex]y=x[/tex]
Transformed function : [tex]c(x)=\dfrac{5}{9}(x-32)[/tex]
Solution:
Let Parent equation be [tex]f(x)=x[/tex]. Then,
[tex]c(x)=\dfrac{5}{9}f(x-32)[/tex] ...(1)
The translation is defined as
[tex]c(x)=kf(x+a)+b[/tex] .... (2)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
On comparing (1) and (2), we get
[tex]k=\dfrac{5}{9}<1[/tex] , So graph of parent function compressed vertically by factor [tex]\dfrac{5}{9}[/tex].
[tex]a=-32<0[/tex], so the graph of parent function shifts 32 units right.
[tex]b=0[/tex], so there is no vertical shift.
Therefore, the graph of parent function compressed vertically by factor [tex]\dfrac{5}{9}[/tex] and shifts 32 units right to get the graph of c(x).
Answer:
A : Horizontal Translation
B: Vertical Compression
Step-by-step explanation:
I did the Edgenuity
Hope this helped :)
