Question

Question 7 PLEASE HELP Describe the transformation from the graph of f(x) =x to the graph of g(x)=1/5x+4 A: The transformations are a rotation and a translation. B: The transformations are a translation, A reflection, and a rotation. C The transformations are a translation and a reflection. D The transformations are a rotation and a reflection

Answer 1

Answer:

  A: The transformations are a rotation and a translation.

Step-by-step explanation:

The function f(x) is shown in the attachment as a dashed red line. The function g(x) is shown as the blue line.

The two lines have different slopes. The change in slope can be accomplished by horizontal or vertical scaling, or by rotation. The offered answer choices only include rotation as an option for changing the slope.

The two lines have different intercepts. To move the line from one intercept to another, generally translation is involved.

The simplest transformation is rotation and translation.

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Comment on the answer choices

If the reflection is done across a line other than an axis, or if the rotation is done about a point other than the origin, then any combination of rotation, reflection, and translation can be used to make the transformation seen. (Translation alone is not sufficient.)

For example, reflecting the line across the bisector of the angle between the lines (a line with a slope of (√13 -2)/3 through (5, 5)) will give the desired transformation in one step.

Similarly, a rotation of about 33.69° about the point (5, 5) will give the transformation in on step. (That angle is 45°-arctan(1/5).)