Question

Write the equation for the given parent function and listed transformations.

Answer 1

We need to find the final equation after the following transformations of the parent function √x:

• reflected across the y-axis;

,

• vertical shrink by 1/3;

,

• up 1;

,

• horizontal shrink by 5/3.

Step-by-step explanation:

• reflected across the y-axis.

When a function is reflected across the y-axis, it's equivalent to replacing x with -x:

`√(x)\rightarrow√(-x)`

• vertical shrink by 1/3.

In order to shrink the function to 1/3 of its original height, we need to multiply the whole expression of the function by 1/3:

`√(-x)\rightarrow(1)/(3)√(-x)`

• up 1.

Now, we need to add 1 to the whole expression of the function:

`(1)/(3)√(-x)\rightarrow(1)/(3)√(-x)+1`

• horizontal shrink by 5/3.

Now, to shink the graph of the function to 5/3 of its original width, we need to multiply x by 5/3:

`(1)/(3)√(-x)+1\rightarrow(1)/(3)\sqrt{-(5)/(3)x}+1`

We can see those transformations in the following graphs:

Answer:

`y=(1)/(3)\sqrt{-(5)/(3)x}+1`