Respuesta :
Answer:
A. [tex]y=\sqrt{x+5}+2[/tex].
Step-by-step explanation:
We are given the function [tex]y=\sqrt{x}[/tex].
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 [tex]f(x)[/tex] to [tex]f(x)+k[/tex].
So, the function translated 2 units up is [tex]y=\sqrt{x}+2[/tex].
Translation of 'k' units to the left changes the function [tex]f(x)[/tex] to [tex]f(x+k)[/tex].
So, the new function translated 5 units left is [tex]y=\sqrt{x+5}+2[/tex].
Hence, the equation representing the new function is [tex]y=\sqrt{x+5}+2[/tex].
y = √(x + 5) + 2
Further explanation
Given:
The graph of [tex]y = \sqrt{x}[/tex] 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:
- [tex]\boxed{ \ y = f(x) + v \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] upward v units.
- [tex]\boxed{ \ y = f(x) - v \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] 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:
- [tex]\boxed{ \ y = f(x + h) \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] to the left h units.
- [tex]\boxed{ \ y = f(x - h) \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] to the right h units.
Therefore, the combination of vertical and horizontal shifts is as follows:
[tex]\boxed{\boxed{ \ y = f(x \pm h) \pm v \ }}[/tex]
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 [tex]y = \sqrt{x}[/tex] is shifted 2 units up.
[tex]\boxed{y = \sqrt{x} \rightarrow is \ shifted \ 2 \ units \ up \rightarrow \boxed{ \ y = \sqrt{x} + 2 \ }}[/tex]
Followed by shifting 5 units left.
[tex]\boxed{y = \sqrt{x} + 2 \rightarrow is \ shifted \ 5 \ units \ left \rightarrow \boxed{ \ y = \sqrt{x + 5} + 2 \ }}[/tex]
Thus, the equation that represents the new graph is [tex]\boxed{\boxed{ \ y = \sqrt{x + 5} + 2 \ }}[/tex]
The answer is A.
Learn more
- 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
- The similar problem of shifting https://brainly.com/question/2488474
- 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
