Each statement describes a transformation of the graph of f(x)=x Which statement correctly describes the graph of g(x) if g(x)=f(x+11) (1) It is the graph of f(x) translated 11 units to the left. It is the graph of f(x) where the slope is decreased by 11. It is the graph of f(x) translated 11 units down. It is the graph of f(x) translated 11 units to the right. ? Question Type the correct answer in each box. The zero (x-intercept) of the parent function, f(x) is square The zero (x-intercept) of the child function, g(x) is square

To determine the transformation of the graph of \( f(x) = x \) to \( g(x) = f(x+11) \), we need to understand how the function \( g(x) = f(x+11) \) affects the graph.<br /><br />1. **Transformation Description:**<br /> - The function \( g(x) = f(x+11) \) represents a horizontal translation of the graph of \( f(x) = x \).<br /> - Specifically, adding 11 inside the function argument translates the graph 11 units to the left.<br /> - Therefore, the correct statement is: "It is the graph of \( f(x) \) translated 11 units to the left."<br /><br />2. **Zero (x-intercept) of the Parent Function \( f(x) \):**<br /> - The parent function \( f(x) = x \) has its zero at \( x = 0 \).<br /><br />3. **Zero (x-intercept) of the Child Function \( g(x) \):**<br /> - For \( g(x) = f(x+11) = x + 11 \), set \( g(x) = 0 \) to find the x-intercept:<br /> \[<br /> x + 11 = 0 \implies x = -11<br /> \]<br /> - Thus, the zero of the child function \( g(x) \) is \( x = -11 \).<br /><br />**Final Answers:**<br /><br />- The zero (x-intercept) of the parent function, \( f(x) \), is \( 0 \).<br />- The zero (x-intercept) of the child function, \( g(x) \), is \( -11 \).