Question

What transformations are used in transforming the parent graph y = x, to obtain the graph of c (x) = StartFraction 5 Over 9 EndFraction (x minus 32)? Check all that apply.

Answer 1

Answer:

A : Horizontal Translation

B: Vertical Compression

Step-by-step explanation:

I did the Edgenuity

Hope this helped :)

Answer 2

Given that:

Parent equation : $y=x$

Transformed function : $c(x)=\dfrac{5}{9}(x-32)$

Solution:

Let Parent equation be $f(x)=x$. Then,

$c(x)=\dfrac{5}{9}f(x-32)$      ...(1)

The translation is defined as

$c(x)=kf(x+a)+b$                .... (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

$k=\dfrac{5}{9}$ , So graph of parent function compressed vertically by factor $\dfrac{5}{9}$.

$a=-32$, so the graph of parent function shifts 32 units right.

$b=0$, so there is no vertical shift.

Therefore, the graph of parent function compressed vertically by factor $\dfrac{5}{9}$ and shifts 32 units right to get the graph of c(x).