Mathematics, 29.01.2020 16:01 vgh641

What transformations change the graph of (f)x to the graph of g(x)?

f(x) = x² ; g(x) = (x + 7)² + 9

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Answer from: mohd591

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.

Further explanation

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:

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

Furthermore in general, 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.,

The combination of vertical and horizontal shifts is as follows:

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

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

Given: $\boxed{ \ f(x) = x^2 \ becomes \ g(x) = (x + 7)^2 + 9 \ }$

We set h = +7 and k = +9.

In the graph, additionally note the shift of points from (0, 0) to (-7, 9).

Conclusion

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.

Learn moreWhat is 270° converted to radians A triangle is rotated 90° about the origin What are the coordinates of the image of point B after the triangle ABC is rotated 270° about the origin?

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

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What transformations change the graph of (f)x to the graph of g(x)?

f(x) = x² ; g(x) =...