Mathematics, 07.10.2019 00:30 oVcper

Which graph represents the following piecewise defined function?

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Answer from: julie426

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.

Answer from: aidenbender06

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?

Answer from: Quest

the most boring ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.

Answer from: Quest

the value of x is 28.2

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