Final answer:
To graph y^2=120/x, you need to consider that this represents a hyperbola, and you must create a table of values excluding x=0, plot the (x, y) data pairs that include both positive and negative y-values, and connect the points to form the two branches of the hyperbola.
Step-by-step explanation:
To graph the equation y^2=120/x, it's helpful to first understand that this is not a standard linear or quadratic equation but a rational equation that might involve two branches of a hyperbola. Here's how you can graph the equation step by step:
- Rewrite the equation to see it more clearly as y = ±sqrt(120/x). Recognize that for every positive value of y, there will be a corresponding negative value of y, which represents the two branches of the hyperbola.
- Create a table of values for x and y by choosing different x-values and solving for the corresponding y-values. Exclude x=0 since division by zero is undefined.
- Plot the data pairs (x,y) onto a coordinate grid. Keep in mind that for every pair (x, y), there is also a pair (x, -y).
- Connect the points smoothly, knowing that this graph lies in two different quadrants because y can take both positive and negative values for a given x.
- Label the graph with f(x) if needed, and make sure to scale the x and y-axes appropriately to accommodate all values you have calculated.
Sketching other equations on the same diagram, like y=x or y=(x-2)/(13), would simply involve repeating the process of creating a table of values for each separate equation and plotting their respective points on the same grid.