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course Phy 241
002. Describing Graphs *********************************************
Question: `q001. You will frequently need to describe the graphs you have constructed in this course. This exercise is designed to get you used to some of the terminology we use to describe graphs. Please complete this exercise and submit your work as instructed.
Note that you should do these graphs on paper without using a calculator. None of the arithmetic involved here should require a calculator, and you should not require the graphing capabilities of your calculator to answer these questions.
Problem 1. We make a table for y = 2x + 7 as follows: We construct two columns, and label the first column 'x' and the second 'y'. Put the numbers -3, -2, -1, -, 1, 2, 3 in the 'x' column. We substitute -3 into the expression and get y = 2(-3) + 7 = 1. We substitute -2 and get y = 2(-2) + 7 = 3. Substituting the remaining numbers we get y values 5, 7, 9, 11 and 13. These numbers go into the second column, each next to the x value from which it was obtained. We then graph these points on a set of x-y coordinate axes. Noting that these points lie on a straight line, we then construct the line through the points.
Now make a table for and graph the function y = 3x - 4.
x y
-3 -13
-2 -10
-1 -7
0 -4
1 -1
2 2
3 5
Identify the intercepts of the graph, i.e., the points where the graph goes through the x and the y axes.
Passes through (0, -4) and (4/3, 0)
`q002. Does the steepness of the graph in the preceding exercise (of the function y = 3x - 4) change? If so describe how it changes.
Your solution: The graphs steepness remains steady. The line neither gets steeper or less steep as ""3"" stays constant
`q003. What is the slope of the graph of the preceding two exercises (the function is y = 3x - 4;slope is rise / run between two points of the graph)?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The slope of the graph is 3/1
`q004. Make a table of y vs. x for y = x^2. Graph y = x^2 between x = 0 and x = 3.
x y
0 0
1 1
2 2
3 9
Would you say that the graph is increasing or decreasing?
It's increasing
Does the steepness of the graph change and if so, how?
the graph gets steeper as the x value increases
Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
increasing at an increasing rate
`q005. Make a table of y vs. x for y = x^2. Graph y = x^2 between x = -3 and x = 0.
x y
-3 9
-2 4
-1 1
0 0
Would you say that the graph is increasing or decreasing?
The graph is decreasing
Does the steepness of the graph change and if so, how?
The graph is getting less steep as the numbers increase.
Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
The graph is decreasing at a decreasing rate.
`q006. Make a table of y vs. x for y = `sqrt(x). [note: `sqrt(x) means 'the square root of x']. Graph y = `sqrt(x) between x = 0 and x = 3.
x y
0 0
1 1
2 1.41
3 1.73
4 2
Would you say that the graph is increasing or decreasing?
The graph is increasing.
Does the steepness of the graph change and if so, how?
The graph gets less steep.
Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
The graph is increasing at a decreasing rate.
`q007. Make a table of y vs. x for y = 5 * 2^(-x). Graph y = 5 * 2^(-x) between x = 0 and x = 3.
x y
0 5
1 2.5
2 1.25
3 0.625
Would you say that the graph is increasing or decreasing?
The graph is decreasing.
Does the steepness of the graph change and if so, how?
The graph becomes less steep with an increasing x value.
Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
The graph is decreasing at a decreasing rate.
`q008. Suppose you stand still in front of a driveway. A car starts out next to you and moves away from you, traveling faster and faster.
If y represents the distance from you to the car and t represents the time in seconds since the car started out, would a graph of y vs. t be increasing or decreasing?
The graph would be increasing.
Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
Increasing at an increasing rate but it would eventually have to level out.
`q009. As you saw above, on the interval from x = -3 to x = 3 the graph of y = x^2 is decreasing at a decreasing rate up to x = 0 and increasing at an increasing rate beyond x = 0.
How would you describe the behavior of the graph of y = (x - 1)^2 between x = -3 and x = 3?
Adding the extra (-1) moves the whole graph up on the axis, changing the origin. the graph itself looks the same.
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