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

The V-graph reveals that

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

graph{y-|2x-3|=0 [-10, 10, -5, 5]}

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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.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What are the points of inflection, if any, of #f(x)=x^(1/3)*(x+3)^(2/3) #?
- For what values of x is #f(x)=(2x-1)(3x-5) (x-2)# concave or convex?
- What are the points of inflection of #f(x)=x^{2}e^{1 -x^2} #?
- How do you find intercepts, extrema, points of inflections, asymptotes and graph #f(x)=x/sqrt(x^2+7)#?
- What are the points of inflection of #f(x)=x^6 + 3x^5 - x^4 - 40x^3 - 60x^2 + 8x + 5 #?

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