How do you find intercepts, extrema, points of inflections, asymptotes and graph #y=abs(2x-3)#?

Question

Christopher Agresta · Accepted Answer

The V-graph reveals that #y=|2x-3|# reveals that vertex v(0, 3/2) gives y-x-intercept as 3/2. The left arm of V creates y-intercept ( x = 0 ) as 3. Vertex is a node.

#y=|2x-3|>=0#. There is no question of looking for asymptotes, for a pair of lines that is self-asymptotic. The common point is a node and, once again, there is no question of looking for point of inflexion. The separate equations for the half lines in this pair are #y=2x-3, x>=3/2 and# #y=-(2x-3), x<=3/2#. graph{y-|2x-3|=0 [-10, 10, -5, 5]}

Ezekiel Alexander · Answer

undefined To find intercepts:
- x-intercept: Set y = 0 and solve for x.
- y-intercept: Set x = 0 and solve for y.

To find extrema:
- Since the absolute value function has corners rather than smooth curves, it doesn't have maxima or minima in the traditional sense.

To find points of inflection:
- The absolute value function doesn't have points of inflection.

To find asymptotes:
- There are no vertical asymptotes.
- Horizontal asymptote: Since the absolute value function approaches positive infinity as x approaches positive infinity, and approaches positive infinity as x approaches negative infinity, there are no horizontal asymptotes.

Graph y = |2x - 3|:
- The graph is a V-shaped graph with the vertex at (1.5, 0) and x-intercept at (1.5, 0). The graph extends indefinitely upwards and downwards from the vertex.