Question

1. the graph of $y = -sqrt{x}$ is shifted 4 units up and 3 units right. which equation represents the new graph?

options:
$y = -sqrt{x - 3} + 4$
$y = -sqrt{x + 3} + 4$
$y = -sqrt{x - 4} + 3$
$y = -sqrt{x + 4} + 3$

Explanation:

Step1: Recall the rules of function transformation

For a function \( y = f(x) \), shifting it \( h \) units to the right and \( k \) units up results in the new function \( y = f(x - h) + k \).

Step2: Identify the original function and the transformations

The original function is \( y = -\sqrt{x} \). We need to shift it 4 units to the right and 3 units up.

Step3: Apply the horizontal shift

For a horizontal shift of 4 units to the right, we replace \( x \) with \( x - 4 \) in the original function. So now we have \( y = -\sqrt{x - 4} \).

Step4: Apply the vertical shift

For a vertical shift of 3 units up, we add 3 to the function we got after the horizontal shift. So the new function is \( y = -\sqrt{x - 4} + 3 \).

Answer:

B. \( y = -\sqrt{x - 4} + 3 \)