Question

The graph of y=√x is shifted 2 units up and 5 units left, Which equation represents the new graph?

Answer 1

y = √(x + 5) + 2

Further explanation

Given:

The graph of $y = \sqrt{x}$ is

• shifted 2 units up, and
• 5 units left.

Question:

Which equation represents the new graph?

The Process:

The translation is a form of transformation geometry.

Translation (or shifting): moving a graph on an analytic plane without changing its shape.

In general, given the graph of y = f(x) and v > 0, we obtain the graph of:  

• $\boxed{ \ y = f(x) + v \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ upward v units.  
• $\boxed{ \ y = f(x) - v \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ downward v units.  

That's the vertical shift, now the horizontal one. Given the graph of y = f(x) and h > 0, we obtain the graph of:  

• $\boxed{ \ y = f(x + h) \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ to the left h units.  
• $\boxed{ \ y = f(x - h) \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ to the right h units.

Therefore, the combination of vertical and horizontal shifts is as follows:  

$\boxed{\boxed{ \ y = f(x \pm h) \pm v \ }}$  

The plus or minus sign follows the direction of the shift, i.e., up-down or left-right.

- - - - - - - - - -

Let's solve the problem.

Initially, the graph of $y = \sqrt{x}$ is shifted 2 units up.

$\boxed{y = \sqrt{x} \rightarrow is \ shifted \ 2 \ units \ up \rightarrow \boxed{ \ y = \sqrt{x} + 2 \ }}$

Followed by shifting 5 units left.

$\boxed{y = \sqrt{x} + 2 \rightarrow is \ shifted \ 5 \ units \ left \rightarrow \boxed{ \ y = \sqrt{x + 5} + 2 \ }}$

Thus, the equation that represents the new graph is $\boxed{\boxed{ \ y = \sqrt{x + 5} + 2 \ }}$

The answer is A.

Learn more

1. Which phrase best describes the translation from the graph y = 2(x – 15)² + 3 to the graph of y = 2(x – 11)² + 3? brainly.com/question/1369568
2. The similar problem of shifting brainly.com/question/2488474  
3. What transformations change the graph of (f)x to the graph of g(x)? brainly.com/question/2415963

Keywords: the graph of, y = √x, shifted 2 units up, 5 units left, which, the equation, represents, the new graph, horizontal, vertical, transformation geometry, translation

Answer 2

Answer:

A. $y=\sqrt{x+5}+2$.

Step-by-step explanation:

We are given the function $y=\sqrt{x}$.

Now, the function is shifted 2 units up and 5 units to the left.

That is, the function is translated 2 units up and 5 units to the left.

Since, we know,

Translation of 'k' units up changes the function $f(x)$ to $f(x)+k$.

So, the function translated 2 units up is $y=\sqrt{x}+2$.

Translation of 'k' units to the left changes the function $f(x)$ to $f(x+k)$.

So, the new function translated 5 units left is $y=\sqrt{x+5}+2$.

Hence, the equation representing the new function is $y=\sqrt{x+5}+2$.