Step-by-step explanation:
To determine which function has the same range as the parent function \(p\), we need to understand how transformations affect the graph of a function.1. The function \(f(x) = p(x+5)\) represents a horizontal shift of the parent function \(p(x)\) to the left by 5 units. This transformation does not affect the range (the set of all possible output or \(y\)-values) of the function, only the domain (the set of all possible input or \(x\)-values).2. The function \(g(x) = 5 + p(x)\) represents a vertical shift of the parent function \(p(x)\) upwards by 5 units. This transformation changes the range by increasing every \(y\)-value in the range of \(p(x)\) by 5.3. The function \(h(x) = p(x) - 5\) represents a vertical shift of the parent function \(p(x)\) downwards by 5 units. This transformation changes the range by decreasing every \(y\)-value in the range of \(p(x)\) by 5.4. The function \(j(x) = 5 - p(x)\) represents a reflection of the parent function \(p(x)\) across the line \(y = 5\). This transformation changes the range in a way that for every \(y\)-value \(y_1\) in the range of \(p(x)\), there is a corresponding \(y\)-value \(y_2 = 5 - y_1\) in the range of \(j(x)\).**Conclusion:**The function that has the same range as the parent function \(p\) is \(f(x) = p(x+5)\), because a horizontal shift does not affect the range of a function.**Accurate Answer:** The function with the same range as the parent function is \(f(x) = p(x+5)\).
