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

To find the absolute maximum and minimum values of the function \( f(x) = 2x - 7 \) over the intervals, we'll evaluate the function at the endpoints and check any critical points within the intervals. ### For interval (A) [0, 5]: 1. **Evaluate at the endpoints**: - \( f(0) = 2(0) - 7 = -7 \) - \( f(5) = 2(5) - 7 = 3 \) 2. **Conclusions**: - The absolute maximum value is \( 3 \) at \( x = 5 \). - The absolute minimum value is \( -7 \) at \( x = 0 \). ### For interval (B) [-4, 5]: 1. **Evaluate at the endpoints**: - \( f(-4) = 2(-4) - 7 = -15 \) - \( f(5) = 3 \) (calculated above) 2. **Conclusions**: - The absolute maximum value is \( 3 \) at \( x = 5 \). - The absolute minimum value is \( -15 \) at \( x = -4 \). ### Final Answers: **(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 \( x = -4 \).