Answered

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

Ay=-√x+5) +2

By=-√x-2) +5

Cy=-√x+2) -5

Dy=-√x-5) +2

Verified Answer :

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 \(y=\sqrt{x+5}+2\).

BladeRunner212

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? https://brainly.com/question/1369568
  2. The similar problem of shifting https://brainly.com/question/2488474  
  3. What transformations change the graph of (f)x to the graph of g(x)? https://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

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