Activity B: Absolute value functions Get the Gizmo ready: Tum off Show derivative. Select Absolute...

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Activity B: Absolute value functions Get the Gizmo ready: • Tum off Show derivative. Select Absolute value function. Tum on Show tangent line. 1. Set a to 1 and b to-2 to graph f(x) = x1-2. (Notice that, for absolute value functions, the tangent line is an extension of one part of the graph.) Drag the red point along the graph. A. What is the equation of the left half of the graph (where x < 0)?_ B. What is the equation of the right half of the graph (where x > 0)? C. What is the derivative (slope) of the left half? D. If the graph of a function has a break in it (a hole or discontinuity), or if it has a sharp turn (like a corner), then the derivative (f(x)) is not defined at that point. Where do you think f(x) for an absolute value function is undefined? E. Based on what you have seen, how would you write the derivative of f(x) = |x|-2? f(x)=_ Explain. Of the right half? Select Show derivative to check. (The light blue graph shows f(x) at all x-values.) F. Vary b. How does b affect the derivative? Explain why this makes sense. G. Vary a and b to see other absolute value functions. In general, what is the derivative of f(x) = ax + b? f(x) =_ 2. Find the derivative of each function. For A-D, check your answers in the Gizmo. A. If f(x) = |x|+4, then f(x) =_ B. If f(x) = -2xl-5, then f(x) = C. If f(x) = 0.5x + 3, then f(x) = D. If f(x)=-1.4|x1| +3.7, then f(x)= E. If f(x) = 4x +31-2, then f(x)= Activity B: Absolute value functions Get the Gizmo ready: • Tum off Show derivative. Select Absolute value function. Tum on Show tangent line. 1. Set a to 1 and b to-2 to graph f(x) = x1-2. (Notice that, for absolute value functions, the tangent line is an extension of one part of the graph.) Drag the red point along the graph. A. What is the equation of the left half of the graph (where x < 0)?_ B. What is the equation of the right half of the graph (where x > 0)? C. What is the derivative (slope) of the left half? D. If the graph of a function has a break in it (a hole or discontinuity), or if it has a sharp turn (like a corner), then the derivative (f(x)) is not defined at that point. Where do you think f(x) for an absolute value function is undefined? E. Based on what you have seen, how would you write the derivative of f(x) = |x|-2? f(x)=_ Explain. Of the right half? Select Show derivative to check. (The light blue graph shows f(x) at all x-values.) F. Vary b. How does b affect the derivative? Explain why this makes sense. G. Vary a and b to see other absolute value functions. In general, what is the derivative of f(x) = ax + b? f(x) =_ 2. Find the derivative of each function. For A-D, check your answers in the Gizmo. A. If f(x) = |x|+4, then f(x) =_ B. If f(x) = -2xl-5, then f(x) = C. If f(x) = 0.5x + 3, then f(x) = D. If f(x)=-1.4|x1| +3.7, then f(x)= E. If f(x) = 4x +31-2, then f(x)=

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a fx 1x12 left of of the graph is line passing through 20 4 0 2 ... View the full answer