How Do You Sketch the Curve of y = f(x) with Given Characteristics?

In summary, the conversation revolves around a problem involving the function f(x) = x^2 - 1. The person is seeking help to obtain various values related to the function such as domain, intercepts, symmetry, asymptotes, intervals of increase/decrease, local maxima and minima, and concavity and points of inflection. They also mention using these values to sketch the curve of y = f(x). The conversation ends with a link to a potential resource for help.
  • #1
drasord
5
0
Hello guys, I'm really stuck on this problem. Could anyone provide help?

f(x) = x^2 - 1

Obtain:
(i) domain
(ii) intercepts
(iii) symmetry
(iv) asymptotes
(v) intervals of increase/decrease
(vi) local maxima and minima
(vii) concavity and points of inflection

Use these values to sketch the curve y = f(x)

Thanks!
 
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  • #2
Before we can offer useful help, we need to know what you have done so far, so we can see where you may be making mistakes or going astray.
 
  • #3
drasord said:
Hello guys, I'm really stuck on this problem. Could anyone provide help?

f(x) = x^2 - 1

Obtain:
(i) domain
(ii) intercepts
(iii) symmetry
(iv) asymptotes
(v) intervals of increase/decrease
(vi) local maxima and minima
(vii) concavity and points of inflection

Use these values to sketch the curve y = f(x)

Thanks!
hello,
Maybe this one Will help http://mathhelpboards.com/calculus-10/how-sketch-graph-function-5159.html

Regards,
\(\displaystyle |\pi\rangle\)
 

FAQ: How Do You Sketch the Curve of y = f(x) with Given Characteristics?

What is calculus sketching a curve?

Calculus sketching a curve is a method used in calculus to graph a function or equation. It involves using principles of calculus, such as derivatives and integrals, to analyze the behavior of a curve and draw an accurate graph.

What are the steps involved in sketching a curve using calculus?

The first step is to analyze the given function or equation using principles of calculus, such as finding derivatives and integrals. Then, determine the critical points, which are points where the slope of the curve changes. Next, find the points of inflection, which are points where the concavity of the curve changes. Finally, use this information to plot the points and sketch the curve.

Why is calculus sketching a curve important?

Calculus sketching a curve is important because it allows us to visualize and understand the behavior of a function or equation. It also helps us to identify important points, such as critical points and points of inflection, which can provide valuable information about the curve.

What are some common challenges when sketching a curve using calculus?

One common challenge is determining the correct behavior of the curve at the critical points and points of inflection. It can also be difficult to accurately plot the curve without making any errors in calculations or graphing. Another challenge is determining the correct scale for the axes to ensure the entire curve is visible on the graph.

Are there any tips for effectively sketching a curve using calculus?

Yes, some tips include: thoroughly understanding the principles of calculus, carefully analyzing the function or equation, double-checking calculations and graphing, and using a graphing calculator or computer software to assist with plotting the curve accurately.

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