The very first thing I'd note is that your "if x = 0" condition is redundant. Specifying that \(f(x) = -2x + 3, \: \text{if} \: 0 \leq x \leq 3\) would suffice because \(f({\color{red}0}) = -2({\color{red}0}) + 3 = 3\). That aside, I agree with your assessment that the portion of the graph in the upper-left quadrant looks like a quarter circle of radius 3. You (should) know that the equation of such a circle (were it complete) is \(x^2 + y^2 = 9\). In order to express this as a function, we want to write it in the form \(y = \text{(something)}\). So, how might you go about solving that equation for \(y\)? What restrictions on \(x\) are necessary to ensure it's a quarter circle rather than a half circle?
Finally, the portion of the graph in the lower-left quadrant also resembles a quarter circle. But what is its radius? What would the equation of that full circle be? How might you solve that for \(y\)? What restrictions on \(x\) are necessary to ensure it's a quarter circle rather than a half circle?
