I don't know how to do this, so I can't graph it. f(x)= 1/x-4
Thank you for the help.
Does that mean 1/(x-4) or (1/x) -4 ?
They are not the same.
Get or draw yourself some graph paper, pick different values of x, and use the value of f(x) that you compute for y.
For example, when x = 5, f(x) = 1/(5-4) = 1
Thank you for answering. It is (1/x)-4. We are asked to use the transformation, to graph the rational function.
I am in an online class, so don't have much help. This is my last math class, thank God! I am not a math person.
Thank you.
If f(x) (1/x)-4, then
y = -3 when x=1,
y = -4.25 when x = 4 and
y = 0 when x = 1/4, etc.
Plot these and various other points that you compute on the graph, and draw a smooth line through them.
At x = 0, the curve goes to + infinity on the right side and to -infinity on the left side of the x axis.
To graph the function f(x) = 1/(x-4), you can follow these steps:
1. Determine the domain: The domain is the set of all possible x-values for which the function is defined. In this case, the function is undefined when the denominator (x-4) equals zero. So, x cannot be equal to 4. Therefore, the domain is all real numbers except x = 4.
2. Identify any vertical or horizontal asymptotes: To determine the vertical asymptote(s), set the denominator equal to zero and solve for x. In this case, x - 4 = 0, so x = 4 is the vertical asymptote.
3. Find the x-intercept(s): To find the x-intercept(s), set the numerator equal to zero and solve for x. However, in this case, the numerator is 1, which can never be equal to zero. So, there is no x-intercept.
4. Determine the y-intercept: To find the y-intercept, substitute x = 0 into the equation. f(0) = 1/(0-4) = 1/(-4) = -1/4. So, the y-intercept is at (0, -1/4).
5. Plot additional points: To graph the function, you can choose a few additional points by substituting different x-values into the equation and calculating the corresponding y-values. For example, when x = 1, f(1) = 1/(1-4) = -1/3. So, one point on the graph is (1, -1/3). Similarly, you can choose more x-values and calculate the corresponding y-values.
6. Sketch the graph: Connect the plotted points with a smooth curve. Since there is a vertical asymptote at x = 4, the graph should approach the asymptote as x gets closer to 4.
Keep in mind that this is a general guide for graphing the function. It's always a good idea to double-check your work by using a graphing calculator or software, if available, to verify the accuracy of the graph.