A graph transformation is when a mathematical function is adjusted or modified in some way, resulting in a change in the shape or position of its graph.
To graph y=1/x, you first plot points on the coordinate plane by choosing various values for x and calculating the corresponding y values. Then, connect the points with a smooth curve to create the graph.
This transformation shifts the graph of y=1/x three units to the left and one unit up. It also changes the shape of the graph, making it more curved near the origin.
This transformation multiplies the x-values by 2 and then subtracts 1 from each x-value before calculating the corresponding y-values. It results in a steeper and narrower graph compared to y=1/x.
To graph y=2x/x-1, you can use the same steps as graphing y=1/x, but with the added transformation of multiplying the x-values by 2 and subtracting 1 from each x-value before calculating the y-values. Alternatively, you can also use the transformations to modify the graph of y=1/x, as explained in question 3.