1. Identify the parent function and describe the transformation for $f(x) = (x + 4)^2$. - Parent function: $y = x^2$ (quadratic function). - Transformation: Horizontal shift left by 4 units. 2. For $h(x) = |x - 3| + 2$. - Parent function: $y = |x|$ (absolute value function). - Transformation: Horizontal shift right by 3 units and vertical shift up by 2 units. 3. For $k(x) = \frac{1}{x} - 18$. - Parent function: $y = \frac{1}{x}$ (rational function). - Transformation: Vertical shift down by 18 units. 4. For $f(x) = \sqrt{x + 1} - 6$. - Parent function: $y = \sqrt{x}$ (square root function). - Transformation: Horizontal shift left by 1 unit and vertical shift down by 6 units. 5. Given the square root function with transformations: translated left 7 and down 12. - Equation: $f(x) = \sqrt{x + 7} - 12$. 6. Given the absolute value function translated 12 units up and 23 units left. - Equation: $f(x) = |x + 23| + 12$. 7. Given the cubic function translated right 3 and up 2. - Parent function: $y = x^3$. - Equation: $f(x) = (x - 3)^3 + 2$. 8. Given the rational function translated right 3 and up 16. - Parent function: $y = \frac{1}{x}$. - Equation: $f(x) = \frac{1}{x - 3} + 16$. 9. For $h(x) = (x + 7)^2 - 1$. - Parent function: $y = x^2$. - Transformations: Horizontal shift left 7 units, vertical shift down 1 unit. - Domain: All real numbers, $(-\infty, \infty)$. - Range: Since the parabola opens upward and vertex is at $(-7, -1)$, range is $[-1, \infty)$. Summary: - Parent functions: quadratic $y=x^2$, absolute value $y=|x|$, rational $y=\frac{1}{x}$, square root $y=\sqrt{x}$, cubic $y=x^3$. - Transformations: horizontal shifts inside the function argument (add/subtract inside parentheses), vertical shifts outside the function (add/subtract). This completes all 9 problems with parent functions, transformations, equations, and domain/range where requested.