The graph of g(x) is obtained by the combination of shifting the graph of f(x) to the left 7 units and upward 9 units.
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Further explanation</h3>
Transformation of a graph: changing the shape and location of a graph.
We already know there are four types of transformation geometry: translation (or shifting), reflection, rotation, and dilation (or stretching).
- The transformation that we will discuss is shifting horizontally or vertically.
- Translation (or shifting): moving a graph on an analytic plane without changing its shape.
- Vertical shift: moving a graph upwards or downwards without changing its shape.
- Horizontal shift: moving a graph to the left or right downwards without changing its shape.
In general, given the graph of y = f(x) and k > 0, we obtain the graph of:
- by shifting the graph of upward k units.
- by shifting the graph of downward k units.
Furthermore in general, given the graph of y = f(x) and h > 0, we obtain the graph of:
- by shifting the graph of to the left h units.
- by shifting the graph of to the right h units.,
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
<u>Given:</u>
We set h = +7 and k = +9.
In the graph, additionally note the shift of points from (0, 0) to (-7, 9).
<u>Conclusion</u>
The graph of g(x) is drawn by the combination of shifting the graph of f(x) to the left 7 units and upward 9 units.
<h3>Learn more</h3>
- What is 270° converted to radians brainly.com/question/3161884
- A triangle is rotated 90° about the origin brainly.com/question/2992432
- What are the coordinates of the image of point B after the triangle ABC is rotated 270° about the origin? brainly.com/question/7437053
Keywords: what transformations, change, the graph of f(x), to the graph of g(x), f(x) = x², g(x) = (x + 7)² + 9, translation, shifting, left, upward