How do you graph the function #y=1/3x^2+1/2x# and identify the domain and range?
See graph below.
Domain:
graph{1/3x^2+1/2x [-1.528, 1.552, 3.08, -1.508]}
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To graph the function ( y = \frac{1}{3}x^2 + \frac{1}{2}x ), follow these steps:
- Plot points using a table of values or use a graphing calculator.
- Sketch the parabolic curve connecting the points.
- Identify the domain as all real numbers (( (-\infty, +\infty) )).
- Determine the range by analyzing the vertex of the parabola and whether it opens upward or downward.
The domain is ( (-\infty, +\infty) ) and the range depends on whether the parabola opens upward or downward. If it opens upward, the range is ( [y_{\text{min}}, +\infty) ), where ( y_{\text{min}} ) is the minimum y-value. If it opens downward, the range is ( (-\infty, y_{\text{max}}] ), where ( y_{\text{max}} ) is the maximum y-value.
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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.
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.
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- How do you write a quadratic equation with -6 and 3/4 as its roots? How do you write the equation in the form #ax^2+ bx+ c =0#, where a, b, and c are integers?

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