Which functions represent a horizontal translation to the left of the parent function f(x) = ln x?Check all that apply.g(x) = 3 ln(x − 1) + 6h(x) = 3 ln(x + 3) + 1r(x) = −3 ln(x + 1) + 3s(x) = −3 ln(x) − 3p(x) = ln(x + 2) − 2

A horizontal shift to the left occurs when x is replaced by x + a, where a is positive. In h(x), ln(x + 3) shifts the parent function left 3 units; in r(x), ln(x + 1) shifts it left 1 unit; and in p(x), ln(x + 2) shifts it left 2 units. The coefficients and added constants cause other transformations but do not change those horizontal shifts. So the correct choices are h(x), r(x), and p(x).

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