Questions: Graph the function y=sqrt(x-19) by plotting points and state the domain and range. Check the results using a graphing calculator.

Solution Steps

The function given is \( y = \sqrt{x - 19} \). The expression inside the square root, \( x - 19 \), must be non-negative for the square root to be defined. Therefore, we have: \[ x - 19 \geq 0 \] \[ x \geq 19 \] Thus, the domain of the function is \( x \in [19, \infty) \).

Since the square root function outputs non-negative values, the range of \( y = \sqrt{x - 19} \) is: \[ y \in [0, \infty) \]

To plot the function, we can choose some values of \( x \) within the domain and calculate the corresponding \( y \) values:

• For \( x = 19 \), \( y = \sqrt{19 - 19} = 0 \).
• For \( x = 20 \), \( y = \sqrt{20 - 19} = 1 \).
• For \( x = 23 \), \( y = \sqrt{23 - 19} = 2 \).
• For \( x = 28 \), \( y = \sqrt{28 - 19} = 3 \).

Final Answer