Which graph represents the following piecewise defined

Ответ:

rschaum08

05.01.2022

The second graph.

Step-by-step explanation:

The first piece of the piecewise function is g(x) = -2x, and it is on the part of the domain defined by x < -2. This means that the point at -2 will not be filled in, since it is strictly less than and not less than or equal to. It also means that the graph will be a line with a slope of -2 from this point backward; this means going backward, the graph will go up two and backward 1.

The second piece of the piecewise function is g(x) = -x². This will be an upside-down parabola (u-shaped graph) that passes through (-1, 1), (0, 0) and (1, -1). It is for the piece of the domain including -2 and going up to but not including 1; this means the left endpoint will be filled in and the right will not.

The third piece of the piecewise function is g(x) = x. This is a straight line with a slope of 1, meaning it goes up 1 and over 1. It is for the part of the domain including 1 and going to the right. This means the endpoint will be filled in.

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Ответ:

janahiac09

05.01.2022

Mathematics

The second graph is the correct match for the piecewise defined function $g\left(x\right)=\left\{ \begin{gathered} - 2x,\,\,\,\,\,\,\,\,\,\,\,\,\,x$ .

Further explanation:

Given:

The given piecewise-defined function is $g\left(x\right)=\left\{ \begin{gathered} - 2x,\,\,\,\,\,\,\,\,\,\,\,\,\,x$ .

Calculation:

The given function is defined as $g\left(x\right)=-2x$ for , $g\left( x \right) =- {x^2}$ for $-2\leq x$ and $g\left( x \right)=x$ for $x\geq1$ .

Therefore, the function is defined over the interval $\left( { - \infty ,\infty }\right)$ .

In the interval $\left( {-\infty ,-2} \right)$ function is a line $g\left( x \right)=-2x$ , over the interval $\left[ {-2,1} \right)$ function gives a parabola $g\left( x \right) =-{x^2}$ and over the interval $\left[ {1,\infty } \right)$ function gives another line as $g\left( x \right)=x$ .

Choose the values of which lies in the interval $\left( {-\infty ,-2} \right)$ and draw a graph for $g\left( x \right) =-2x$ .

Choose the values of which lies in the interval $\left[ {-2,1} \right)$ and draw a graph for $g\left( x \right) =-{x^2}$ .

Again choose the values of which lies in the interval $\left( { -\infty ,- 2} \right)$ and draw a graph for $g\left( x \right) =x$ .

The table for the values of and the corresponding values the function $g\left( x \right) =-2x$ is shown below in Table 1.

The table for the values of and the corresponding values the function $g\left( x \right) =-{x^2}$ is shown below in Table 2.

The table for the values of and the corresponding values the function $g\left( x \right) = x$ is shown below in Table 3.

Now the graph of piecewise-defined function $g\left(x\right)=\left\{ \begin{gathered} - 2x,\,\,\,\,\,\,\,\,\,\,\,\,\,x$ is sketched in Figure 1.

Thus, the second graph is the correct match for the piecewise defined function $g\left(x\right)=\left\{ \begin{gathered} - 2x,\,\,\,\,\,\,\,\,\,\,\,\,\,x$ .

Learn more:

1. Which function has an inverse that is also a function? {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}

2. A given line has the equation 10x + 2y = −2. what is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)? y = ( )x + 12

3. what are the domain and range of the function f(x) = 3x + 5?

Answer Details :

Grade: SeniorSchool .

Subject: Mathematics .

Chapter: Function.

Keywords:

lines, parabola, straight lines, g(x),function, piecewise defined function, graph, domain, intervals, intercepts, function value, intercepts of lines, slope, slope intercept form, continuous, range, point, y=-2x,y=x,y=x^2.

Which graph represents the following piecewise defined function?

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Ответ:

KariSupreme

28.01.2020

Mathematics

A zero, since no force is necessary to keep it moving

Step-by-step explanation:

Since, the space is friction less, the force exerted by the gun will be enough to keep the ball going. There will not be any depreciation in the initial force. Hence, the ball continues to move forward without any impediment.

Hence, the correct answer is

A zero, since no force is necessary to keep it moving

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