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Marta_Voda [28]

2 years ago

6

What is the range of A piecewise function g of x, where part 1 is x squared plus 5 for x greater than 2 and part 2 is 2 times x

for x greater than or equal to 2.?
[4, ∞)
[5, ∞)
[9, ∞)
(–∞, ∞)

1 answer:

____ [38]2 years ago

6 0

Using it's concept, it is found that the range of the piece-wise function is given by:

[4, ∞)

<h3>What is the range of a function?</h3>

It is the set that contains all possible output values for the function.

A piece-wise function has multiple definitions.

For x < 2, we have that f(x) = x² + 5, hence the range is from 5(smallest value, when x = 0) to infinity.

For x >= 2, we have that f(x) = 2x, and the range is from 4(smallest value, when x = 2) to infinity.

Combining them, the range of the entire function is given by:

[4, ∞)

More can be learned about the range of a function at brainly.com/question/10891721

#SPJ1

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Show Your Work!<br> Will Mark Brainliest!

salantis [7]

Answer:

The Graph Shifts 4 units up

Step-by-step explanation:

Okay so, when you add four to a graph in this manner we have to look at the equation as a whole. f(x)=mx+b + 4. By adding four we are changing the y-intercept and shifting it up four. This will cause the entire graph to shift upwards four spaces.

8 0

3 years ago

Find the vertex of the graph of the function.

lapo4ka [179]

Answer: The correct options are (1) (5,10), (2) (3,-3), (3) x = -1, (4) $y=(x+2)^2+3$ , (5) 21s and (6) 0, -1, and 5.

Explanation:

Te standard form of the parabola is,

$f(x)=a(x-h)^2+k$ .....(1)

Where, (h,k) is the vertex of the parabola.

(1)

The given equation is,

$f(x)=(x-5)^2+10$

Comparing this equation with equation (1),we get,

$h=5$ and $k=10$

Therefore, the vertex of the graph is (5,10) and the fourth option is correct.

(2)

The given equation is,

$f(x)=3x^2-18x+24$

$f(x)=3(x^2-6x)+24$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $9$ . Since there is factor 3 outside the parentheses, so subtract three times of 9.

$f(x)=3(x^2-6x+9)+24-3\times 9$

$f(x)=3(x-3)^2-3$

Comparing this equation with equation (1),we get,

$h=3$ and $k=-3$

Therefore, the vertex of the graph is (3,-3) and the fourth option is correct.

(3)

The given equation is

$f(x)=4x^2+8x+7$

$f(x)=4(x^2+2x)+7$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $1$ . Since there is factor 4 outside the parentheses, so subtract three times of 1.

$f(x)=4(x^2+2x+1)+7-4$

$f(x)=4(x+1)^2+3$

Comparing this equation with equation (1),we get,

$h=-1$ and $k=3$

The vertex of the equation is (-1,3) so the axis is x=-1 and the correct option is 2.

(4)

The given equation is,

$y=x^2+4x+7$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $2^2$ .

$f(x)=x^2+4x+4+7-4$

$f(x)=x^2+4x+4+7-4$

$f(x)=(x+2)^2+3$

Therefore, the correct option is 4.

(5)

The given equation is,

$h=-16t^2+672t$

It can be written as,

$h=-16(t^2-42t)$

It is a downward parabola. so the maximum height of the function is on its vertex.

The x coordinate of the vertex is,

$x=\frac{b}{2a}$

$x=\frac{42}{2}$

$x=21$

Therefore, after 21 seconds the projectile reach its maximum height and the correct option is first.

(6)

The given equation is,

$f(x)=3x^3-12x^2-15x$

$f(x)=3x(x^2-4x-5)$

Use factoring method to find the factors of the equation.

$f(x)=3x(x^2-5x+x-5)$

$f(x)=3x(x(x-5)+1(x-5))$

$f(x)=3x(x-5)(x+1)$

Equate each factor equal to 0.

$x=0,-1,5$

Therefore, the zeros of the given equation is 0, -1, 5 and the correct option is 2.

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3 years ago

What is the speed (approximately) of a 2.5-kilogram mass after it has fallen freely from rest through a distance of 12 meters?

Norma-Jean [14]

Answer:

15.3 m/s

Step-by-step explanation:1) Find the gravitational potential energy using the equation :

$PE_g=mgh$

$PE_g=2.5(12)(9.8)\\PE_g=294$

2) Then use the equation for kinetic energy to solve for the velocity:

$KE=\frac{1}{2} mv^{2}$

$294=\frac{1}{2}(2.5)(v^2)\\235.2=v^2\\\sqrt{235.2} =v\\15.3 m/s=v$

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3 years ago

Multiply.<br> (-0.3)(-0.85)

Neporo4naja [7]

Answer:

O.225

Step-by-step explanation:

Two negatives = positive

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3 years ago

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Classify the polygon as regular or irregular, and concave or convex.

Svetradugi [14.3K]

Answer:

This would be a regular polygon.

Step-by-step explanation:

A regular polygon has congruent sides and interior angles.

An irregular polygon does not have congruent sides and all interior angles.

A convex polygon does not have a interior angle greater than 180°.

Lastly, a concave polygon has only one interior angle greater than 180°.

Using the process of elimination, it would not be a convex or concave polygon. Now we have either a regular or irregular polygon. This polygon can not be a irregular polygon because all the sides are congruent. This means that this polygon is a regular polygon!

7 0

3 years ago