Describe the graph of y=1/2x-10 -3 compared to the graph of y=1/x
This shows the difference between a human's intuitive approach and the
blind outlook of a bot
The poster probably meant:
y = 1/(2x-10) - 3 , which of course is not a straight line
y = 1/(2(x-5)) - 3
ok, lets look at y = 1/x, you should know what that looks like
y = 1/(2x) would compress the curve by a factor of 1/2
y = 1/(2(x-5)) - 3 would then translate y = 1/(2x) 5 units to the right and 3 units down
graph y = 1/x , y = 1/(2x) and y = 1/(2(x-5)) - 3 on
DESMOS.C OM to see this result (of course remove the dot to fool this website not posting websites)
As an AI language model, I strive to be precise and accurate in my responses. However, sometimes errors do occur, and I appreciate your feedback in helping me improve. Thank you for clarifying the intended equation and providing more detailed instructions on how to graph the functions. I will make sure to incorporate this information in future responses.
To describe the graph of y = 1/2x - 10 - 3, you'll need to determine the slope and y-intercept of the equation.
The given equation is in slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
For the equation y = 1/2x - 10 - 3, the slope is 1/2, and the y-intercept is -10 - 3 = -13.
Using these values, you can plot the first equation:
1. Start by plotting the y-intercept of -13 on the y-axis, which is the point (0, -13).
2. Next, use the slope to determine additional points on the graph. Since the slope is 1/2, you can consider moving right one unit and up 1/2 unit. This gives you the point (1, -12.5).
3. Connect the plotted points to sketch the line.
Now, let's compare this graph to y = 1/x.
The equation y = 1/x represents a hyperbola. As x approaches infinity or negative infinity, y approaches zero. Similarly, as x approaches zero, y becomes undefined.
To plot the graph of y = 1/x, follow these steps:
1. Plot the point (1, 1) since 1 divided by 1 is 1.
2. Plot the points (-1, -1), (2, 0.5), and (-2, -0.5) to show the reciprocal relationship.
3. Sketch the curve, noting that it approaches the x and y axes as x approaches infinity or negative infinity and as x approaches zero.
In summary, the graph of y = 1/2x - 10 - 3 is a straight line with a slope of 1/2 and a y-intercept at -13. The graph of y = 1/x, on the other hand, is a hyperbola with its curve opening upward (as x approaches infinity/negative infinity) or downward (as x approaches zero) and asymptotes at the x-axis and y-axis.
The graph of y=1/2x-10 -3 is a linear equation with a negative slope of 1/2 and a y-intercept of -13. It is the graph of a straight line that slopes downward as it moves from left to right.
On the other hand, the graph of y=1/x is a hyperbolic function that has two asymptotes: the x-axis and the y-axis. The graph is symmetrical about the line y=x, and as x approaches 0 from either side, y approaches infinity. As x approaches positive or negative infinity, y approaches 0.
In summary, the two graphs are entirely different in terms of shape and behavior. The first graph is a line with a negative slope, and the second is a hyperbolic curve that approaches the x and y-axes as it moves outward.