Sketch the graphs of f(x)=3overx+1 and g(x)=-2x-4 on the same set of axes
I am sure you meant
f(x) = 3/(x+1)
http://www.wolframalpha.com/input/?i=plot+y+%3D+3%2F%28x%2B1%29+%2C+y+%3D-2x-4
look at the 2nd graph, the vertical blue line is an anymptote
To sketch the graphs of the functions f(x) and g(x) on the same set of axes, follow these steps:
Step 1: Plot the points:
Start by choosing a few x-values and finding the corresponding y-values for each function. This will help you to plot some points on the graph.
For f(x) = 3/(x + 1), let's choose x-values of -3, -2, -1, 0, 1, 2, and 3:
Substituting each x-value into the equation, we can find the corresponding y-values:
For x = -3, f(-3) = 3/(-3 + 1) = 3/(-2) = -3/2
For x = -2, f(-2) = 3/(-2 + 1) = 3/(-1) = -3
For x = -1, f(-1) = 3/(-1 + 1) = 3/0 --> Here, f(-1) is undefined as division by zero is undefined.
For x = 0, f(0) = 3/(0 + 1) = 3/1 = 3
For x = 1, f(1) = 3/(1 + 1) = 3/2
For x = 2, f(2) = 3/(2 + 1) = 3/3 = 1
For x = 3, f(3) = 3/(3 + 1) = 3/4
Now, let's do the same for g(x) = -2x - 4. Choose a few x-values and find the corresponding y-values:
For x = -3, g(-3) = -2(-3) - 4 = 6 - 4 = 2
For x = -2, g(-2) = -2(-2) - 4 = 4 - 4 = 0
For x = -1, g(-1) = -2(-1) - 4 = 2 - 4 = -2
For x = 0, g(0) = -2(0) - 4 = 0 - 4 = -4
For x = 1, g(1) = -2(1) - 4 = -2 - 4 = -6
For x = 2, g(2) = -2(2) - 4 = -4 - 4 = -8
For x = 3, g(3) = -2(3) - 4 = -6 - 4 = -10
Step 2: Plot the points on a graph:
Take a set of axes and plot the points you found for both f(x) and g(x). Coordinate points are represented as (x, y), where x is the x-value and y is the y-value.
For f(x), plot the points (-3, -3/2), (-2, -3), (0, 3), (1, 3/2), and (2, 1). Remember that the point (-1, f(-1)) is undefined as f(-1) is not defined.
For g(x), plot the points (-3, 2), (-2, 0), (-1, -2), (0, -4), (1, -6), (2, -8), and (3, -10).
Step 3: Connect the points with a smooth curve:
Using a ruler or by freehand, draw a smooth curve that passes through all the plotted points for each function. Be sure to extend the curves beyond the plotted points to represent the behavior of the functions beyond the range of plotted values.
The final graph should show the curves of f(x) and g(x) intersecting the x-axis, changing direction at certain points, and making their way through different regions of the coordinate plane.