Final Answer:
The given function y = -x - 3, limited to the domain x < 8 and x > -8, creates a range of y-values between -5 and -1 inclusively. This range is obtained by evaluating the function at the domain's boundaries, resulting in the minimum and maximum values that y can take within the specified domain. Therefore, the range of the graph lies within the interval y > -5 and y < -1.
Thus the correct option is c.
Step-by-step explanation:
The given function y = -x - 3 represents a linear equation with a slope of -1 and a y-intercept of -3. Since the domain is restricted to x < 8 and x > -8, the range of the graph needs to be determined within this domain.
When x < 8 and x > -8, let's find the corresponding y-values:
- For x = -8, y = -(-8) - 3 = 8 - 3 = 5
- For x = 8, y = -(8) - 3 = -8 - 3 = -11
Hence, as x ranges from -8 to 8, y varies from 5 to -11. However, within the given domain, the range lies between the maximum and minimum y-values obtained for these x-values.
Therefore, the range of the graph within the domain x < 8 and x > -8 is y > -5 and y < -1.
The given function represents a straight line with a negative slope. The restriction of the domain to x < 8 and x > -8 limits the x-values and consequently limits the y-values of the graph. By evaluating the function at the endpoints of this restricted domain, the maximum and minimum values for y are obtained. These values define the range of the graph within the specified domain. In this case, the range is determined to be y > -5 and y < -1. This means that the graph of the function will fall within this range for the given domain, depicting the vertical span of the function's output.
Thus the correct option is c.