Graph each function. \( \begin{array}{ll}\text { 28. } f(x)=x-1 & \text { 29. } 12-x-2 y=0 \\ \text { 31. } y=x^{2}-2 & \text { 32. } x^{2}-y=-4 \\ \text { 34. } f(x)=|2 x|-2 & \text { 35. } y=|-x| \\ \text { 37. Find the value of } x \text { so that }(x, 12) \text { satisfies } y=4 x+8 \text {. } \\ \text { 38. Find the value of } x \text { so that }(x, 6) \text { satisfies } y=-x-4 \text {. } \\ \text { 39. Find the value of } y \text { so that }(-2, y) \text { satisfies } y=-2 x^{2} \text {. }\end{array} \)

Solve the equation by following steps: - step0: Solve for \(y\): \(y=-8\) Solve the equation \( 6=-x-4 \). Solve the equation by following steps: - step0: Solve for \(x\): \(6=-x-4\) - step1: Swap the sides: \(-x-4=6\) - step2: Move the constant to the right side: \(-x=6+4\) - step3: Add the numbers: \(-x=10\) - step4: Change the signs: \(x=-10\) Solve the equation \( 12=4*x+8 \). Solve the equation by following steps: - step0: Solve for \(x\): \(12=4x+8\) - step1: Swap the sides: \(4x+8=12\) - step2: Move the constant to the right side: \(4x=12-8\) - step3: Subtract the numbers: \(4x=4\) - step4: Divide both sides: \(\frac{4x}{4}=\frac{4}{4}\) - step5: Divide the numbers: \(x=1\) It seems that I am unable to plot the functions directly. However, I can provide you with the solutions for the equations and describe how to graph the functions. ### Solutions for the Equations 1. **For the equation \( y = 4x + 8 \) with the point \( (x, 12) \)**: - We set \( 12 = 4x + 8 \). - Solving gives \( x = 1 \). 2. **For the equation \( y = -x - 4 \) with the point \( (x, 6) \)**: - We set \( 6 = -x - 4 \). - Solving gives \( x = -10 \). 3. **For the equation \( y = -2x^2 \) with the point \( (-2, y) \)**: - We set \( y = -2(-2)^2 \). - Solving gives \( y = -8 \). ### Descriptions of the Functions to Graph 1. **\( f(x) = x - 1 \)**: This is a linear function with a slope of 1 and a y-intercept of -1. It will be a straight line that crosses the y-axis at -1. 2. **\( 12 - x - 2y = 0 \)**: Rearranging gives \( y = \frac{12 - x}{2} \). This is also a linear function with a slope of -0.5 and a y-intercept of 6. 3. **\( y = x^2 - 2 \)**: This is a quadratic function that opens upwards with its vertex at (0, -2). 4. **\( x^2 - y = -4 \)**: Rearranging gives \( y = x^2 + 4 \). This is another upward-opening parabola with its vertex at (0, 4). 5. **\( f(x) = |2x| - 2 \)**: This is a V-shaped graph that opens upwards, with the vertex at (0, -2). 6. **\( y = |-x| \)**: This is also a V-shaped graph that opens upwards, with the vertex at (0, 0). ### Summary of Values Found - \( x \) for \( (x, 12) \) in \( y = 4x + 8 \) is \( 1 \). - \( x \) for \( (x, 6) \) in \( y = -x - 4 \) is \( -10 \). - \( y \) for \( (-2, y) \) in \( y = -2x^2 \) is \( -8 \). If you need further assistance or specific details about any of the functions, feel free to ask!