Question

What transformations have been made from the parent gach f(z)=logz togs f(z)=log-z+8)-5A reflection in the x-axis, vertical stretch by 1/2, 3 units in the x-direction, and 4 units in the y-directionOB. reflection in the y-aris, vertical stretch by 112, -3 units in the x-direction, and 4 units in the y-directionOC reflection in the y-aris, vertical stretch by 1/2, 3 units in the x-direction, and 4 units in the y directionOP reflection the yer verica stretch by 1.12.-23 units in the direction, and 4 units in the x-direction

Answer 1

GIVEN:

We are given the parent function,

$f(x)=logx$

And this has been transformed to get another function,

$f(x)=\frac{1}{2}log(-x+3)-4$

Required;

To identify the transformations that have been made from the parent function.

Step-by-step solution;

To identify the transformations that have taken place, observe the following;

When the parent function is multiplied by a value, then its vertically stretched, hence we have a vertical stretch by 1/2.

When the parent function is switched from x to negative x, then we have a reflection in the y axis.

Also when a parent function is changed

$\begin{gathered} From; \\ f(x)=x \\ \\ To; \\ f(x)=(x+h) \end{gathered}$

The rules of transformations states that this is a movement minus h units along the x-axis.

Therefore we have, -3 units in the x direction.

And also, when the parent function is changed

$\begin{gathered} From; \\ f(x)=x \\ \\ To; \\ f(x)=(x)-h \end{gathered}$

The rules of transformations states that is a movement h units down the y-axis.

Therefore, we have, -4 units along the y-axis.

Therefore, for the function of the graph given, we have;

ANSWER:

$\begin{gathered} Reflection\text{ }in\text{ }y-axis \\ \\ Vertical\text{ }stretch\text{ }by\text{ }\frac{1}{2} \\ \\ -3\text{ }units\text{ }in\text{ }the\text{ }x\text{ }direction \\ \\ -4\text{ }units\text{ }in\text{ }the\text{ }y\text{ }direction \end{gathered}$

Option B is the correct answer