The text on the screen is as follows:---"Suppose that the function \( g \) is defined, for all real numbers, as follows.\[g(x) = \begin{cases} -1 & \text{if } x \neq 0 \\-2 & \text{if } x = 0 \end{cases}\]Graph the function \( g \)."---Below the text, there is a coordinate plane with the x-axis and y-axis. The graph is expected to represent the function \( g(x) \) as defined above. Explanation of the graph:- For all values of \( x \) not equal to 0, \( g(x) = -1 \). This means the graph will have a horizontal line at \( y = -1 \) for \( x \neq 0 \).- At \( x = 0 \), \( g(x) = -2 \). Therefore, there will be a distinct point at \( (0, -2) \).- The graph will show a continuous line at \( y = -1 \) with an isolated point at \( (0, -2) \).To visually distinguish \( x = 0 \), you might see a filled or open circle on the graph to represent the change in value. The problem statement is as follows:Suppose that the function \( f \) is defined for all real numbers as follows:\[f(x) = \begin{cases} 1 - x^2 & \text{if} \ x < 1 \\ -2x - 3 & \text{if} \ x \geq 1 \end{cases}\]You are asked to graph the function \( f \). Then determine whether or not the function is continuous.### Explanation of the Graph:The graph on the screen appears to consist of two parts:1. **Quadratic Function**: \( f(x) = 1 - x^2 \) for \( x < 1 \) - This portion of the graph is part of a downward opening parabola. It will have its vertex at the point (0, 1) and crosses the x-axis at x = ±1. Only the section for \( x < 1 \) is relevant here.2. **Linear Function**: \( f(x) = -2x - 3 \) for \( x \geq 1 \) - This part of the graph is a straight line with a negative slope. It passes through the point (1, -5) and continues downward.You should evaluate the function at \( x = 1 \) to determine continuity:- From the left (using \( 1 - x^2 \)), \( f(1^{-}) = 1 - 1^2 = 0 \)- From the right (using \(-2x - 3\)), \( f(1^{+}) = -2(1) - 3 = -5 \)Since the limits from the left and right do not match, the function is discontinuous at \( x = 1 \).The screen also includes graphing tools, such as line, curve, and point selectors, indicating that you can use these to construct the graph visually.

Answered: Suppose that the function g is defined,…

Suppose that the function g is defined, for all real numbers, as follows. if x+0 -1 g(x) = -2 if x= 0 Graph the function g.

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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