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

Question

asked Nov 21, 2023 215k views

1 Answer

Dan Alexander · Answer 1 · 2023-11-28T06:38:41+0000

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:

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