Find the absolute maximum and minimum values of the function over the indicated interval, and indicate the \( x \)-values at which they occur. \( f(x)=2 \mathrm{x}-7 \) \( \begin{array}{ll}\text { (A) }[0,5] & \text { (B) }[-4,5] \\ \text { The absolute minimum value is } \square \text { at } x=9 \text {. } \\ \text { (Use a comma to separate answers as needed.) } \\ \text { (A) The absolute maximum value is } \square \text { at } \mathrm{x}=\square \text {. } \\ \text { (B) The absolute maximum value is } \square \text { at } \mathrm{x}=\square \\ \text { (Use a comma to separate answers as needed.) } \\ \text { The absolute minimum value is } \square \text { at } \mathrm{x}=\square \\ \text { (Use a comma to separate answers as needed.) }\end{array} \)

To find the absolute maximum and minimum values of the function \( f(x) = 2x - 7 \) over the intervals given, we need to evaluate the function at the endpoints and check if there are any critical points within the interval. For interval \( (A) [0,5] \): 1. Calculate \( f(0) = 2(0) - 7 = -7 \) 2. Calculate \( f(5) = 2(5) - 7 = 3 \) The absolute maximum value is \( 3 \) at \( x = 5 \), and the absolute minimum value is \( -7 \) at \( x = 0 \). For interval \( (B) [-4,5] \): 1. Calculate \( f(-4) = 2(-4) - 7 = -15 \) 2. Calculate \( f(5) = 2(5) - 7 = 3 \) The absolute maximum value is still \( 3 \) at \( x = 5 \), and the absolute minimum value is \( -15 \) at \( x = -4 \). So, the filled values are: - (A) The absolute maximum value is \( 3 \) at \( x = 5 \), The absolute minimum value is \( -7 \) at \( x = 0 \). - (B) The absolute maximum value is \( 3 \) at \( x = 5 \), The absolute minimum value is \( -15 \) at \( x = -4 \).