Watch the video and then solve the problem given below. Click here to watch the video. Evaluate the function \( f(x)=x^{2}+5 x-7 \) at the given values of the independent variable and simplify. \( \begin{array}{lll}\text { a. } f(-3) & \text { b. } f(x+6) & \text { c. } f(-x)\end{array} \) a. \( f(-3)=\square \) (Simplify your answer.)

To evaluate \( f(-3) \), we substitute \(-3\) into the function: \[ f(-3) = (-3)^2 + 5(-3) - 7 = 9 - 15 - 7 = -13. \] So, \( f(-3) = -13 \). To evaluate \( f(x+6) \), we replace \( x \) with \( x + 6 \): \[ f(x+6) = (x + 6)^2 + 5(x + 6) - 7. \] Expanding this gives: \[ = (x^2 + 12x + 36) + (5x + 30) - 7 = x^2 + 12x + 5x + 36 + 30 - 7 = x^2 + 17x + 59. \] So, \( f(x+6) = x^2 + 17x + 59 \). Now, to evaluate \( f(-x) \), we substitute \(-x\) into the function: \[ f(-x) = (-x)^2 + 5(-x) - 7 = x^2 - 5x - 7. \] Thus, \( f(-x) = x^2 - 5x - 7 \). The answers are: a. \( f(-3) = -13 \) b. \( f(x+6) = x^2 + 17x + 59 \) c. \( f(-x) = x^2 - 5x - 7 \)