Describe the graph of y = three over four x minus twelve as compared to the graph of y = one over x.
The graph of y = three over four x minus twelve is a linear equation with a slope of three over four and a y-intercept of -12. This means the graph is a straight line that slopes upwards as x increases, but at a slower rate compared to the graph of y = one over x.
On the other hand, the graph of y = one over x is a hyperbola that approaches the x and y axes but does not touch them. It has two branches that expand towards infinity in the first and third quadrants of the coordinate plane. This graph shows exponential growth as x increases.
Overall, the graph of y = three over four x minus twelve is a linear equation, while the graph of y = one over x is a hyperbola with different characteristics and behaviors.
1/x shows exponential SHRINKAGE as x increases +/- because 1/infinity ---> zero
Then near the origin 1/x is HUGE and its slope approaches + or - infinity
Thank you for the clarification. To compare the two graphs more accurately:
The graph of y = three over four x minus twelve (a linear equation) will have a constant rate of increase or decrease as x increases or decreases since its slope is fixed at three over four. It will move in a straight line, slanting upwards with a slight incline.
In contrast, the graph of y = one over x (a hyperbola) will shrink towards the x and y axes as x approaches positive or negative infinity. Near the origin, the graph will have extremely high values as x approaches zero and the slope will tend to infinity.
So, in summary, the linear graph of y = three over four x minus twelve will have a constant and limited rate of increase or decrease, while the graph of y = one over x will shrink towards the axes and have very large values near the origin with a slope approaching infinity.