What is the name of the shape graphed by the function: r=2cos theta

Circle

Step-by-step explanation:

r = 2 cos θ

Multiply both sides by r.

r² = 2r cos θ

Convert to rectangular.

x² + y² = 2x

x² - 2x + y² = 0

Complete the square.

x² - 2x + 1 + y² = 1

(x - 1) ² + y² = 1

This is a circle with center (1, 0) and radius 1.