Questions: a. State the domain and range of each function. b. Use the graph to estimate the impact energy of each metal at 0°C. Use the graph of each function to find its y-intercept and zero(s). Then find these values algebraically. (Examples 3 and 4)

Solution Steps

For problem 16, the function given is \( f(x) = \sqrt{x - 1} \).

To find the y-intercept, set \( x = 0 \) and solve for \( y \): \[ f(0) = \sqrt{0 - 1} \] Since the square root of a negative number is not defined in the real number system, there is no y-intercept for this function.

To find the x-intercept(s), set \( f(x) = 0 \) and solve for \( x \): \[ 0 = \sqrt{x - 1} \] Square both sides: \[ 0 = x - 1 \] \[ x = 1 \] So, the x-intercept is at \( (1, 0) \).

The function \( f(x) = \sqrt{x - 1} \) is defined for \( x - 1 \geq 0 \), so: \[ x \geq 1 \] Thus, the domain is \( [1, \infty) \).

The range of the function is all non-negative real numbers since the square root function outputs non-negative values: \[ [0, \infty) \]

Final Answer