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2 years ago

What is the range of the radical function f(x) = to the square root of x-2 +4

Mathematics

1 answer:

jarptica [38.1K]2 years ago

6 0

Answer:

2,∞

Step-by-step explanation:

For the range, x2 takes its minimum at x=0 , so putting in x =0 gives y=√x2+4=√0+4=2 therefore making the range [2,∞).

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Find the value of x when m<2 = x + 64

polet [3.4K]

Answer:

-9

Step-by-step explanation:

The triangle has two sides that are the same, so it is an isosceles triangle. Therefore, the base angles are the same.

Angles of a triangle add up to 180°, so:

70 + (x + 64) + (x + 64) = 180

70 + 2x + 128 = 180

2x = -18

x = -9

5 0

3 years ago

Read 2 more answers

Write an equation for a quadratic function that has x intercepts (-3, 0) and (5, 0)

Blizzard [7]

Answer:

One possible equation is $f(x) = (x + 3)\, (x - 5)$ , which is equivalent to $f(x) = x^{2} - 2\, x - 15$ .

Step-by-step explanation:

The factor theorem states that if $x = x_{0}$ (where $x_{0}$ is a constant) is a root of a function, $(x - x_{0})$ would be a factor of that function.

The question states that $(-3,\, 0)$ and $(5,\, 0)$ are $x$ -intercepts of this function. In other words, $x = -3$ and $x = 5$ would both set the value of this quadratic function to $0$ . Thus, $x = -3\!$ and $x = 5\!$ would be two roots of this function.

By the factor theorem, $(x - (-3))$ and $(x - 5)$ would be two factors of this function.

Because the function in this question is quadratic, $(x - (-3))$ and $(x - 5)$ would be the only two factors of this function. In other words, for some constant $a$ ( $a \ne 0$ ):

$f(x) = a\, (x - (-3))\, (x - 5)$ .

Simplify to obtain:

$f(x) = a\, (x + 3)\, (x - 5)$ .

Expand this expression to obtain:

$f(x) = a\, (x^{2} - 2\, x - 15)$ .

(Quadratic functions are polynomials of degree two. If this function has any factor other than $(x - (-3))$ and $(x - 5)$ , expanding the expression would give a polynomial of degree at least three- not quadratic.)

Every non-zero value of $a$ corresponds to a distinct quadratic function with $x$ -intercepts $(-3,\, 0)$ and $(5,\, 0)$ . For example, with $a = 1$ :