Off-topic Comments Section All top-level comments have to be an answer or follow-up question to the post. All sidetracks should be directed to this comment thread as per Rule 9. OP and Valued/Notable Contributors can close this post by using /lock command I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns. More on reddit.com

K, let's look. Obvious g'(x) = 0 -> g(x) is constant on the interval g'(x) < 0 -> g(x) is decreesing on the interval obvious obvious g''(x) > 0 -> g(x) is convex on the interval g''(x) < 0 -> g(x) is concave on the interval However, there are contradictions. f.e. second and third: g'(x) = 0 on (-2,2) since (-2,2) ⊂ (-∞, 2) and also g'(x) < 0 on (-2,2) And there are more. So it is impossible to construct that function. More on reddit.com

Off-topic Comments Section All top-level comments have to be an answer or follow-up question to the post. All sidetracks should be directed to this comment thread as per Rule 9. PS: u/happychicken05 , your post is incredibly short! body <200 char You are strongly advised to furnish us with more details. OP and Valued/Notable Contributors can close this post by using /lock command I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns. More on reddit.com

You can graph with Desmos . Here's an example: https://www.desmos.com/calculator/xrfmngtyoi . The syntax for defining a piecewise function should be clear from the example above, but to be explicit: f(x) = {[condition 1 on x]: [expression 1], [condition 2 on x]: [expression 2]}. The absolute value function over the reals would then be f(x) = {x >= 0: x, x < 0: -x} After defining your piecewise functions, plot the composition by adding the equation of that graph, i.e., if you've defined f and g, add the equation y = f(g(x)) or y = g(f(x)) to see the composition. More on reddit.com