Can I take the voltage across diode to be same as the input voltage in a limiting circuit?
In the textbook when the input is between +5 and -5 both diodes are reverse biased so they do not conduct and the signal crcuit is just a 10K resistor, 

in the case when either diode is forwards biased the signal now encounters a resistive divider.

So you get  \$ V_i + 5 \over 2 \$ or \$ v_i + -5 \over 2 \$ depending on which diode is conducting

In your circuit, 

the the diodes are pointing upwards so vith voltages above that from the most positive source (the right leg) wich is 5V neither diode will conduct and input will equal output, 
with voltages below that first the one diode will conduct (the right one)  but as the voltage gets more negative it's not until -15V in that the output gets to -5  and only then doe the other diode conduct. 

with this type of circuit the transfer function should be continuous, that's a simple check you can apply to your answers.

for your circuit one way to derive the transfer function is to consider how much current must flow through the input resistor to produce each output voltage, by considering it that way you can see that -5V out needs -1ma and thus -15V