Question

Which graph represents the following piecewise defined function?

Answer 1

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

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

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

The table for the values of $x$ 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)}  

brainly.com/question/1632445  

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  

brainly.com/question/1473992  

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

brainly.com/question/3412497  

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.

Answer 2

Answer:

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.