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The Hebrew verb רָחַם râcham (Strong's #7355, x47) "to have mercy" and its corresponding noun רַחַם racham (Strong's #7356, x44) "mercy, compassion, womb, bowels" are probably best known from the prophetic drama of the naming of Hosea's daughters in Hosea 1:6 and later reversed in Hosea 2:1:
"And she conceived again and bore a daughter. Then God said to him: 'Call her name Lo-Ruchamah, For I will no longer have mercy [râcham] on the house of Israel, but I will utterly take them away.'" (Hosea 1:6)
רָחַם râcham is a favourite word of Isaiah (x12), Jeremiah (x9) and Hosea (x6), accounting for nearly 60% of its usage.
The first instance of this word is in Exodus 33:19, "[I] will be gracious to whom I will be gracious, I will shew mercy on whom I will shew mercy" (KJV), translated by "compassion" in the NKJV and the NIV; the latter leaves itself few options for it translates the first verb in the phrase as "mercy" instead of the usual "be gracious" from חָנַן chânan (Strong's #2603). The Greek Septuagint similary struggles to translate "grace" and uses "mercy" and then resorts to "compassion" for רָחַם râcham. The Hebrew verbs here are Piel intensives in form suggesting an extended intense overflowing of mercy. They are again used alongside חָנַן chânan in 2 Kings 13:23; Psalm 102:13; Isaiah 27:11; 30:18.
The phrase "show you mercy, have compassion on you", found in Deuteronomy 13:17, is actually "give you רַחַם racham and have רָחַם râcham on you", pairing the noun with the verb, rather than different verbs as in Exodus 33:19 above.
If it God's nature to have mercy and ours to imitate it is nonetheless clear though that God cannot be the subject of our mercy to others. This causes us to pause, therefore, before translating Psalm 18:1, David's reflection on God's mercy to him in saving him from Saul. Here we have David exclaiming, אֶרְחָמְך erechâm'kâ, usually rendered by, "I will love You, O LORD". Clearly, David cannot have mercy on God. On occasions רָחַם râcham almost seems to be an opposite to anger and wrath, so perhaps David is expressing relief and is no longer angry towards God.
Indeed, Gesenius' Lexicon sees the simple qal form of the verb meaning as "to be soft", extending to "mercy" in the piel/pual intensive forms of the verb. In fact, only here in Psalm 18:1 does the verb occur in any form apart from the piel/pual intensive forms. Brown, Driver & Briggs, see the original root meaning as dubious and mention "softness", "wide, spaciousness" and hint at an unclear relationship with רֶחֶם rechem (Strong's #7358) "womb", which would explain the motherly reference below.
The love in view on other occasions is both fatherly - Psalm 103:13 "As a father pities/has compassion on his children, So the LORD pities those who fear Him", (cf. Jeremiah 31:20 where the verb is repeated for additional intensity, רַחֵםאֲרַחֲמֶנּוּ rachêm arachamennû "surely have mercy"); and motherly - Isaiah 49:15 "Can a woman forget her nursing child, And not have compassion on the son of her womb?
The semantic domain in several contexts is the receipt of grace and forgiveness as shown in Proverbs 28:13, "He who covers his sins will not prosper, But whoever confesses and forsakes them will receive mercy" (cf. Isaiah 55:7; Micah 7:19). This mercy extends to the weak and defenceless, such as children (Isaiah 13:18) and the fatherless (Hosea 14:3), whether they have sinned or not, so the word is not only used in salvation from sin but also rescue from physical danger and distress.
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