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y = √(x + 5) + 2
<h3>Further explanation</h3><u>Given:</u>
The graph of is
- shifted 2 units up, and
- 5 units left.
<u>Question:</u>
Which equation represents the new graph?
<u>The Process:</u>
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:
by shifting the graph of
upward v units.
by shifting the graph of
That's the vertical shift, now the horizontal one. Given the graph of y = f(x) and h > 0, we obtain the graph of:
by shifting the graph of
by shifting the graph of
Therefore, the combination of vertical and horizontal shifts is as follows:
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 is shifted 2 units up.
Followed by shifting 5 units left.
Thus, the equation that represents the new graph is
The answer is A.
<h3>Learn more</h3>- 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
- The similar problem of shifting brainly.com/question/2488474
- 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
