What is the graph of the function f(x)=−⌊x⌋
1 answer:
Answer:
Step-by-step explanation:
The equation being shown in the question is the absolute value of x. Absolute values when graphed show up as a V-shaped graph pointing upwards. This is because whatever value is passed as an input will output a positive, regardless of whether the input is positive or negative. Meaning that both 4 and -4 will output 4. That is why the graph is a V-shaped because the outputs repeat for both positive and negative inputs. In this case since the negative is outside the absolute value brackets the positive value given from the absolute value of the input will be turned into a negative. So this will cause the V-shape graph to be reflected across the x-axis. As seen in the attached picture below.
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A slope also known as the gradient of a line is a number. The correct option is A, C, and D.
<h3>What is Slope?</h3>A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
For the given question,
- The temperature increased until 4:00 p.m.
This can be observed in the graph, as the slope of the graph before 4 pm is positive, it can be concluded that the temperature is increased until 4 pm.
- The temperature decreased after 6:00 p.m.
This can be observed in the graph, as the slope of the graph after 4 pm is negative, it can be concluded that the temperature is decreasing after 4 pm.
- The temperature increased more quickly between 12:00 p.m. and 4:00 p.m. than before 12:00 p.m.
This can be probed by calculating the slope of the line between the two points. Therefore, the slope between 8 am to 12 pm will be 1, while the slope from 12 pm to 4 pm will be equal to 4/3.
Hence, the correct option is A, C, and D.
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