Plot the graph of y=3-x and y= 3 tan x on the same plane
To plot the graphs of y = 3-x and y = 3tan(x) on the same plane, we can start by creating a table of values for x and calculating the corresponding y-values for each equation.
Let's start with the first equation, y = 3 - x:
x | y
--------
-3 | 6
-2 | 5
-1 | 4
0 | 3
1 | 2
2 | 1
3 | 0
Now, let's calculate the values for y = 3tan(x):
x | y
---------
-π | 0
-π/2 | undefined (as tan(-π/2) = ∞)
0 | 0
π/2 | undefined (as tan(π/2) = ∞)
π | 0
3π/2 | undefined (as tan(3π/2) = ∞)
2π | 0
Note: The tan function is undefined at odd multiples of π/2, so we have undefined y-values for those x-values.
Now, let's plot the points for each equation and draw the lines:
For y = 3 - x:
Plot the points (-3, 6), (-2, 5), (-1, 4), (0, 3), (1, 2), (2, 1), (3, 0) and draw a straight line passing through these points.
For y = 3tan(x):
Plot the points (-π, 0), (0, 0), (π, 0), (2π, 0) and draw a straight line passing through these points. However, note that the points (-π/2, undefined) and (π/2, undefined) should not be plotted.
The resulting graph should show both lines on the same plane.
To plot the graphs of y = 3 - x and y = 3 tan x on the same plane, we will first determine the range of x-values over which we want to plot them.
Let's start with the first equation: y = 3 - x.
To plot this line, we need two points. We can choose any two values of x and substitute them into the equation to find the corresponding y-values.
Let's choose x = 0.
Plugging this into the equation, we get:
y = 3 - 0 = 3.
So, one point on the line is (0, 3).
Next, let's choose x = 2.
Plugging this into the equation, we get:
y = 3 - 2 = 1.
So, another point on the line is (2, 1).
Now, let's plot these two points and draw a line passing through them.
Moving on to the second equation: y = 3 tan x.
This is a trigonometric function, and its graph will repeat periodically.
Let's determine the behavior of the graph by considering a few x-values and their corresponding y-values.
When x = 0, y = 0.
When x = π/4, y = 3 tan(π/4) = 3 * 1 = 3.
When x = π/2, y = 3 tan(π/2) = 3 * ∞ (approaching infinity).
Now, let's plot these points.
Note that for values of x greater than π/2 or less than 0, the graph will continue to repeat in periodic cycles.
Now, we can plot both graphs on the same plane.
Remember to label the axes and include appropriate scales.