In the above diagram, suppose the equation of curve A is Which of the following is a possible equation for curve B?
In the above diagram, A is a circle with radius centered at the origin and B is an ellipse with major axis and minor axis centered at If B is stretched and translated to obtain A, which of the following processes should be applied?
(i) Translate B by and in the positive directions of the -axis and -axis, respectively, and stretch by a factor of with respect to the -axis.
(ii) Translate B by and in the positive directions of the -axis and -axis, respectively, and stretch by a factor of with respect to the -axis.
(iii) Translate B by and in the positive directions of the -axis and -axis, respectively, and stretch by a factor of with respect to the -axis.
(iv) Translate B by and in the positive directions of the -axis and -axis, respectively, and stretch by a factor of with respect to the -axis.
Every point on the curve is shifted to a new point by the translation where and are integers. The set of forms the curve . What is the value of ?
Given the graph , which of these statements describes the transformations to get the graph of for ?
Translate to the left by 1 and up by , then scale vertically by 2.
Translate to the left by and up by , then scale vertically by 2.
Translate to the left by 1 and up by , then scale vertically by 2.
Translate to the left by and up by , then scale vertically by 2.
Given the graph , what is the sequence of operations required to obtain the graph of
Note: The above graph is not drawn to scale.
(i) Stretch the given graph by a factor of with respect to the -axis and translate by in the positive direction of the -axis.
(ii) Stretch the given graph by a factor of with respect to the -axis and translate by in the positive direction of the -axis.
(iii) Stretch the given graph by a factor of with respect to the -axis and translate by in the positive direction of the -axis.
(iv) Stretch the given graph by a factor of with respect to the -axis and translate by in the positive direction of the -axis.