Analyze the effect on the \( x \)-intercept of the graph of \( f(x)=\sqrt[3]{x} \) when \( f(x) \) is replaced by \( f(x+c) \) and \( c \) is positive. (1 point). The \( x \)-intercept shifts left by a distance of \( c \). The \( x \)-intercept shifts down by a distance of \( c \). The \( x \)-intercept shifts up by a distance of \( c \). The \( x \)-intercept shifts to the right by a distance of \( c \).

When we replace \( f(x) \) with \( f(x+c) \), we are effectively shifting the graph horizontally. For the function \( f(x) = \sqrt[3]{x} \), the original \( x \)-intercept occurs where \( f(x) = 0 \), which is at \( x = 0 \). By replacing it with \( f(x + c) \), we are shifting the graph to the left by \( c \) units. Therefore, the new \( x \)-intercept will be at \( x = -c \). So, the correct answer is: The \( x \)-intercept shifts left by a distance of \( c \).