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4 years ago

What the domain and range is for the function f(x) = x2 + 4x - 21.

Mathematics

1 answer:

prisoha [69]4 years ago

7 0

Answer:

Step-by-step explanation:

Please use " ^ " to denote exponentiation: f(x) = x^2 + 4x - 21.

This function has a graph which is a parabola that opens up.

Its vertex is found by completing the square:

x² + 4x + 4 - 4 - 21, or

(x + 2)² - 25

Comparing this to the standard equation

(x - h)² + k, we see that h = -2 and k = -25.

Thus, the vertex (and the minimum of this function) is (-2, -25).

Thus, the range is [-25, ∞ ). This being a polynomial function, it has no restrictions on the domain: the domain is (-∞, ∞ )

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$2\frac{1}{6}\approx 2.167$ units.

Step-by-step explanation:

We have been given that Joy recorded the distances she walked each day for five days.

To find the distance traveled be Joy in 5 days we will add the distances covered by Joy each day.

As there are 3 dots on 1/3, this means that Joy traveled 1/3 units on 3 days.

Since there is 1 dot on 1/2 and on dot on 2/3, so this means that Joy walked 1/2 units one day and 2/3 units another day.

Let us add all these distances.

$\text{Total distance walked by Joy in 3 days}=3\times\frac{1}{3}+\frac{1}{2}+\frac{2}{3}$

$\text{Total distance walked by Joy in 3 days}=\frac{1*3}{3}+\frac{1}{2}+\frac{2}{3}$

Let us have a common denominator.

$\text{Total distance walked by Joy in 3 days}=\frac{3*2}{3*2}+\frac{1*3}{2*3}+\frac{2*2}{3*2}$

$\text{Total distance walked by Joy in 3 days}=\frac{6}{6}+\frac{3}{6}+\frac{4}{6}$

$\text{Total distance walked by Joy in 3 days}=\frac{6+3+4}{6}$

$\text{Total distance walked by Joy in 3 days}=\frac{13}{6}$

$\text{Total distance walked by Joy in 3 days}=2\frac{1}{6}$

Therefore, Joy traveled $2\frac{1}{6}\approx 2.167$ units in 5 days.

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4 years ago