CH_3-CH=CH-CH_2-COOH What is the IUPAC name of the above compound ?

Identify the principal functional group, which is the carboxylic acid group ($\text{-COOH}$).

Number the carbon chain starting from the carboxylic acid carbon to give it the lowest locant ($1$).

The numbering is as follows:
$\text{C}^5\text{H}_3\text{-C}^4\text{H=C}^3\text{H-C}^2\text{H}_2\text{-C}^1\text{OOH}$

The longest chain has $5$ carbon atoms, so the root word is pent.

There is a double bond starting at carbon $3$, so the primary suffix is $3$-en.

The secondary suffix for the carboxylic acid is oic acid.

Combining these parts, the IUPAC name is pent-$3$-enoic acid.

Answer: Pent-3-enoic acid