Unraveling the Mystery of y=1+x+x^3

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In summary, the conversation is about understanding domains and ranges in a function. The domain is the set of all possible x values that do not cause problems, while the range is the set of all possible y values the function can take on. It is important to consider the behavior of the function as x approaches infinity and negative infinity. The problem is simpler than it may seem, unless it involves the inverse function.
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qablos
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y=1+x+x3I just don't know where to begin...
I've always struggled with domains and ranges.

Even if you could just point me in the right direction, that would be great!

Thanks.
 
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The domain is the set of all possible x values for your function which don't cause problems. Think about this, are there any x values which your function will have a problem?

As for the range, it's the set of all possible y values your function can take on. Do your y values take on all of the real numbers or are there some which are not included?
 
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  • #3


Look at what happens to y as x goes to infinity and as x goes to negative infinity. This is problem is much simpler than I suspect you realize! If the problem were about the inverse function, that would be another matter.
 

FAQ: Unraveling the Mystery of y=1+x+x^3

What is the equation y=1+x+x^3?

The equation y=1+x+x^3 is a polynomial equation with three terms. The first term is a constant, the second term is a linear term, and the third term is a cubic term.

What is the meaning of the variables in y=1+x+x^3?

The variable y represents the output or dependent variable, while the variable x represents the input or independent variable. In this equation, x is raised to the powers of 1 and 3, which means it is a quadratic function.

What is the significance of the constant term in y=1+x+x^3?

The constant term, 1, is the y-intercept of the graph of this equation. It represents the value of y when x is equal to 0. In other words, it is the starting point of the graph.

How is the graph of y=1+x+x^3 different from other polynomial graphs?

The graph of y=1+x+x^3 is a cubic function, which means it has a distinctive "S" shape. This is different from linear and quadratic functions, which have a straight line and a parabola shape, respectively.

How can we use the equation y=1+x+x^3 in real-life applications?

The equation y=1+x+x^3 can be used to model various real-life phenomena, such as population growth, financial investments, and physical processes. It can also be used to make predictions and solve problems in fields such as engineering, physics, and economics.

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