How do you find the domain and range for #x^2 + 5x + 6#?

Answer 1
#f(x) = x^2 + 5x + 6 = (x + 2)(x + 3)#

minimum coordinates of the vertex

#x = -b/21 = -5/2# #y = f(-5/2) = 25/4 - 25/2 + 6 = -1/4#

Range for y: (-1.4, +infinity); Domain for x: (-infinity, +infinity)

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Answer 2

The domain of the function ( f(x) = x^2 + 5x + 6 ) is all real numbers, denoted as ( (-\infty, \infty) ). The range depends on whether the parabola opens upwards or downwards. If it opens upwards, the range is ( [k, \infty) ), where ( k ) is the y-coordinate of the vertex. If it opens downwards, the range is ( (-\infty, k] ). To determine the direction, check the coefficient of ( x^2 ): if it's positive, the parabola opens upwards; if it's negative, it opens downwards. Then, use the vertex formula to find the y-coordinate of the vertex.

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Answer from HIX Tutor

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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