# parent function and composition transformation

**Question description**

**1.
**Consider the following transformations on parent function f(x) =sqr root X

*y = A(x)* which shifts *3* units left;

*y = B(x)* which shifts the graph down by *2 *units

*y = C(x)* which reflects a graph over the *x*-axis

*y= D(x)* which stretches the function
vertically by a factor of *5*

A. For each transformation above, write
as a function of *x*.

B. For each of the following six compositions, on graph paper, sketch/label the parent, and then on the same pair of axes, sketch/label each intermediate function, with its equation, as well as the final composition.

* (i) A *then *B* then *C*;
(ii) *C* then *B* then C *; *(iii) *D* then *C* then *D;*

(iv) *B*
then *D* then *B; *(v) *D* then *B* then *D; (vi) B then C then B*

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