All categories

3 years ago

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

Mathematics

1 answer:

prisoha [69]3 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 (-∞, ∞ )

You might be interested in

a pet store buys bags of dog food for 30.00 dollars per bag and sells them for 54.00 dollars per bag. What is the percent markup

Alenkinab [10]

Answer:

80%

Step-by-step explanation:

(54-30)/30 *100 = 80%

7 0

3 years ago

Identify the type of conic section that has the equation 9x2+ 16y2 = 144 and identify its domain and range.

Kobotan [32]

9 x² + 16 y² = 144 /:144
$\frac{ x^{2} }{16} + \frac{ y^{2} }{9} =1$
General formula of ellipse ( the center is at the origin ): $\frac{ x^{2} }{ a^{2} }+ \frac{ y^{2} }{ b^{2} } =1$
a² = 16, b² = 9
Domain: [-a, a ] = [-4, 4]
Range:[-b, b ]
Answer: B ) ellipse.
Domain: { -4 ≤ x ≤ 4 }
Range: { -3 ≤ y ≤ 3 }

8 0

2 years ago

A cone-shaped paper cup can hold 35 cubic inches of food. If the radius of the cone is 2.4 inches, what is the height of the con

SVETLANKA909090 [29]

$\bf \textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}~~
\begin{cases}
r=radius\\
h=height\\
-----\\
r=2.4\\
V=35
\end{cases}\implies 35=\cfrac{\pi (2.4)^2 h}{3}\implies 105=5.76\pi h
\\\\\\
\cfrac{105}{5.76\pi }=h\implies 5.805467091295 \approx h\implies 5.81 \approx h$

7 0

2 years ago

Read 2 more answers

Find d: ??? Ft. Plz help idk this question

gavmur [86]

Check the picture below.

8 0

2 years ago

Solve the following equation. Round solution to the tenths place. 29 = с/7.2 C =

expeople1 [14]

Answer:

c = 208.8

Step-by-step explanation:

a. $\frac{c}{7.2} =29$ To solve for C, you need to get the variable on one side of the equation and the numbers on the other side of the equation.

b. $\frac{c}{7.2} =29$ You need to move the 7.2 to the other side. So, multiply both sides by 7.2, because it's being divided, so multiplying will cancel it out.

c: $c = 29 * 7.2$ Then, multiply 7.2 by 29. (The * symbol means multiply)

d. c. = 208.8 The answer is 208.8, which is rounded to the tenths place.

Hope this helps! I tried to explain it in detail. :)

7 0

3 years ago