1. Describe how the graphs of y=|x| and y=|x|-15 are related.
2. Graph y=|x|-2.
3. Graph y=-|x-4|.
4. Write an equation for the translation of y=|x|, 2 units down.
5. Graph the equation by translating y=|x|, y=|x+7|
I use mathway for quick checks after brainly and jiskha... Just saying
#1,2,4: translation up or down is done by adding or subtracting from y.
If y = f(x)
then y = f(x) +3 shifts the graph up.
#3: reflection through the x-axis is done by changing the sign of y. What was above goes below, etc.
y = -f(x) reflects f(x) through the x-axis.
#5: replacing x with (x-h) shifts the graph to the right.
replacing x by (x+h) shifts to the left by h.
There are lots of good online graphing sites.
desmos and wolframalpha come to mind.
Enter your functions and see what happens.
1. The graphs of y = |x| and y = |x| - 15 are related in that the latter graph is shifted vertically downward by 15 units compared to the former. Both graphs have the same shape, which resembles the letter V, with its vertex at the origin (0,0).
2. To graph y = |x| - 2, start by plotting the vertex at (0, -2). Then, for all x-values greater than 0, the y-values are equal to the corresponding x-values minus 2. For example, if x = 1, then y = |1| - 2 = 1 - 2 = -1. Connect the points on the graph to form a V-shape.
3. To graph y = -|x - 4|, start by plotting the vertex at (4, 0). Then, for all x-values less than 4, the y-values are equal to the negative of the corresponding x-values minus 4. For example, if x = 3, then y = -|3 - 4| = -|-1| = -1. Connect the points on the graph to form a V-shape opening downward.
4. The equation for the translation of y = |x|, 2 units down is y = |x| - 2. This equation represents the same V-shaped graph as y = |x|, but it is shifted 2 units downward.
5. To graph y = |x| and y = |x + 7| on the same coordinate plane, start by plotting the vertex of y = |x| at (0, 0). Then, plot the vertex of y = |x + 7| at (-7, 0). Both graphs have the same shape, resembling a V-shape, but they are horizontally shifted. Connect the points on each graph to represent the V-shaped curves, showing how the graphs are related.
1. To describe the relationship between the graphs of y=|x| and y=|x|-15, we can start by looking at the equation y=|x| first. The graph of y=|x| is a V-shaped graph that passes through the origin (0,0) and is symmetric with respect to the y-axis. It represents the absolute value of x, which means that it gives the distance of any x-value from the origin (0,0).
Now, let's consider the equation y=|x|-15. By subtracting 15 from the absolute value of x, we shift the entire graph of y=|x| downward by 15 units. This means that the new graph, y=|x|-15, has the same V-shape but is now 15 units below the original graph at any given x-value. The graph of y=|x|-15 still retains the symmetry with respect to the y-axis that characterized the original graph.
2. To graph y=|x|-2, start by identifying a few key points on the graph.
When x = 0, y = |0| - 2 = -2. So, one point on the graph is (0, -2).
For positive x-values, y = |x| - 2. So, if x = 1, y = |1| - 2 = 1 - 2 = -1. Another point on the graph is (1, -1).
Similarly, for negative x-values, y = |x| - 2. So, if x = -1, y = |-1| - 2 = 1 - 2 = -1. Another point on the graph is (-1, -1).
Plotting these points on a coordinate plane and connecting them will give you the graph of y=|x|-2, which is a V-shaped graph shifted 2 units downward from the graph of y=|x|.
3. To graph y=-|x-4|, you can again start by identifying key points on the graph.
When x = 4, y = -|4-4| = -|0| = 0. So, one point on the graph is (4, 0).
For x-values greater than 4, y = -|x-4|. So, if x = 5, y = -|5-4| = -|1| = -1. Another point on the graph is (5, -1).
Similarly, for x-values less than 4, y = -|x-4|. So, if x = 3, y = -|3-4| = -|-1| = -(-1) = 1. Another point on the graph is (3, 1).
Plotting these points on a coordinate plane and connecting them will give you the graph of y=-|x-4|, which is an upside-down V-shaped graph centered at x = 4.
4. To write an equation for the translation of y=|x|, 2 units down, we need to shift the original graph downward by 2 units. Since the shift is downward, we subtract 2 from the absolute value function y=|x|.
Therefore, the equation for the translated graph is y = |x| - 2.
5. To graph the equation by translating y=|x| to y=|x+7|, we need to shift the original graph 7 units to the left.
Start by identifying key points on the graph of y=|x|. For example, when x = 0, y = |0| = 0. So, one point on the original graph is (0, 0).
To shift 7 units to the left, subtract 7 from the x-values of each point. So, the translated point becomes (-7, 0).
Continue this process for other key points on the original graph and translate them 7 units to the left. Then, plot these translated points on a coordinate plane and connect them to obtain the graph of y=|x+7|.