g. \( y=2 \sqrt{x}+10 \)

1. **Domain:** The square root function \( \sqrt{x} \) is defined when \[ x \ge 0, \] so the domain of the function is \[ x \ge 0. \] 2. **Range:** Since for \( x \ge 0 \) we have \( \sqrt{x} \ge 0 \) and \[ y = 2\sqrt{x} + 10, \] the smallest value of \( y \) occurs when \( \sqrt{x} = 0 \), giving \[ y = 2(0) + 10 = 10. \] Thus, the range is \[ y \ge 10. \] 3. **Finding \( x \) in terms of \( y \):** Starting with the equation \[ y = 2\sqrt{x} + 10, \] subtract 10 from both sides: \[ y - 10 = 2\sqrt{x}. \] Divide both sides by 2: \[ \frac{y - 10}{2} = \sqrt{x}. \] Square both sides to solve for \( x \): \[ x = \left(\frac{y - 10}{2}\right)^2. \] 4. **Intercepts:** - **Y-intercept:** Set \( x = 0 \). Then, \[ y = 2\sqrt{0} + 10 = 10. \] So, the y-intercept is at \( (0, 10) \). - **X-intercept:** Set \( y = 0 \). Then, \[ 0 = 2\sqrt{x} + 10. \] Subtract 10 from both sides: \[ -10 = 2\sqrt{x}, \] and divide by 2: \[ -5 = \sqrt{x}. \] Since \( \sqrt{x} \) cannot be negative, there is no x-intercept. The function \( y = 2\sqrt{x} + 10 \) is completely characterized by these properties.