Question

Which of the following is a result of shifting a circle with equation (x + 3)2 + (y - 2)2 = 36 up 3 units? A. The x-coordinate of the center of the circle increases by 3. B. The y-coordinate of the center of the circle decreases by 3. C. Both the x- and y-coordinates of the center of the circle increase by 3. D. The y-coordinate of the center of the circle increases by 3.

Answer 1

D.

Explanation:

Answer 2

D. (y-2) becomes (y-5) and -5 < -2

Explanation:

When transforming functions, the following applies:

• Adding/subtracting inside the parenthesis to the input shifts the function left(+) and right(-).

• Adding/subtracting outside the parenthesis to the output shifts the function up(+) and down(-).

• Multiplying the function by a number less than 1 compresses it towards the x-axis.

• Multiplying the function by a number greater than 1 stretches it away from the x-axis.

In this situation, the circle is shifted up 3 units and the variable y which controls this is in the function. To move it up you will subtract 3 in the parenthesis for (y-2) so it becomes (y-5). This will move the vertex 3 units higher.