f(x)= 1/(x+2)
i have to graph this, can some one please help me!
I answered this below
Please do not confuse me by posting the same problkem again and again
Algebra II - Damon, Monday, July 4, 2011 at 3:51pm
x , f(x)
-5 , -1/3
-4 , -1/2
-3 , -1
-2.5 , - 2
-2 undefined denominator of zero
-1.5 , +2
-1 , +1
0 , +1/2
1 , +1/3
Sure, I'd be happy to help you graph the function f(x) = 1/(x+2).
To graph this function, you can follow these steps:
Step 1: Determine the domain of the function. In this case, the function is defined for all values of x except when the denominator, (x+2), equals zero. So, x + 2 ≠ 0. Solving for x, we find x ≠ -2. Therefore, the domain of the function is all real numbers except -2.
Step 2: Determine the vertical asymptote(s). Vertical asymptotes occur where the function approaches positive or negative infinity. Since the denominator (x+2) cannot equal zero, there is a vertical asymptote at x = -2.
Step 3: Determine the horizontal asymptote. A horizontal asymptote is a horizontal line that the function approaches as x tends towards positive or negative infinity. For this function, as x approaches positive or negative infinity, the function tends towards 0. Therefore, there is a horizontal asymptote at y = 0.
Step 4: Find the x-intercept(s) and y-intercept(s). To find the x-intercept, set y (or f(x)) equal to zero and solve for x. So, 1/(x+2) = 0. Since the numerator of the fraction is always 1, the function will never equal zero. Therefore, there are no x-intercepts. To find the y-intercept, set x equal to zero and solve for y. So, f(0) = 1/(0+2) = 1/2. The y-intercept is (0, 1/2).
Step 5: Choose some x-values and find the corresponding y-values to plot additional points for the graph. You can choose various x-values (except -2) and use the function f(x) = 1/(x+2) to find the corresponding y-values. For example, if you choose x = -3, you can find f(-3) = 1/(-3+2) = -1. If you choose x = 0, you can find f(0) = 1/(0+2) = 1/2. And so on.
Step 6: Plot the points obtained from step 4 and step 5. Also, plot the vertical asymptote at x = -2 and the horizontal asymptote at y = 0.
Step 7: Draw a smooth curve passing through the plotted points and approaching the asymptotes as necessary.
And there you have it! You have successfully graphed the function f(x) = 1/(x+2).