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A horizontal translation is a shift of a graph along the $x$-axis. This means we have to manipulate the inputs of the original function. To move a function $f(x)$ by $h$ units to the left, we have to add $h$ to the function's inputs. We get: $f(x+h).$ We want the graph of $g(x)$ to be a horizontal translation $3$ units to the left of the graph of $f(x).$ This means we have to add $3$ to $x:$ $g(x)=f(x+3).$

b

A reflection is a transformation that flips a graph over a line called the line of reflection. A reflection in the $x$-axis, means that the $x$-values stay the same, but the signs of the $y$-values are changed. To change the sign of the outputs from the function we have to multiply the function by $-1.$ $g(x)=-1⋅f(x)⇔g(x)=-f(x)$