Describe the graph of y=1/2x-10 -3 compared to the graph of y=1/x

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To describe the graph of y = 1/2x - 10 compared to the graph of y = 1/x, we need to look into their key characteristics and compare them.

1. Gradient (Slope):
The first equation, y = 1/2x - 10, has a gradient of 1/2. This means that for every unit increase in the x-axis, the y-value increases by 1/2. The slope in this case is positive.

On the other hand, the second equation, y = 1/x, has a gradient that varies depending on the x-value. However, it will always be positive. As the x-value increases, the gradient (or slope) gets smaller and smaller, but it never becomes negative.

2. Y-intercept:
In the equation y = 1/2x - 10, the y-intercept is -10. This means that the graph intersects the y-axis at the point (0, -10).

For the equation y = 1/x, there is no y-intercept since the graph approaches but never reaches the y-axis. The graph of y = 1/x starts in quadrant 1 and extends infinitely towards the positive x and y-axis.

3. Behavior as x approaches infinity and negative infinity:
For the equation y = 1/2x - 10, as x approaches infinity, the graph approaches the x-axis with a positive slope. As x approaches negative infinity, the graph approaches the x-axis with a negative slope.

For the equation y = 1/x, as x approaches infinity (both positive and negative), the graph approaches the x and y-axes. As x approaches zero from the positive or negative side, the graph extends towards positive and negative infinity.

Overall, the graph of y = 1/2x - 10 is a straight line with a positive slope and a y-intercept of -10. The graph of y = 1/x is a curve that starts in quadrant 1, approaches but never reaches the x and y-axes, and extends infinitely towards the positive and negative x and y-axis.

y = 1/(2x-10) - 3

= 1/(2(x-5)) - 3
= (1/2) * 1/(x-5) - 3

Now can you see the scaling and shifting?