How to Graph y = 9/x² Without a Calculator?

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In summary, the graph of the equation y= 9/x2 can be approximated by noting its symmetry and asymptotes, and replacing x with y and y with x will reflect the graph through the line y= x.
  • #1
Integral0
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(1) How do you graph the equation y = 9 divided by x^2 w/o using a calculator and besides plotting points?

(2) If you replace x with y and y with x, can you reflect the equation 9/x^2 ?

thanks
 
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  • #2
You can't graph an equation (other than a linear equation) exactly without plotting individual points.

You can get a pretty good approximation by noting that, since x2 is always positive, y= 9/x2 is above the y-axis and symmetric about the x axis. Of course, for x close to 0, y will be very large: the y-axis is a vertical asymptote. For x very large, y is close to 0: the x-axis is a horizontal asymptote.

(2) If you replace x with y and y with x, can you reflect the equation 9/x^2 ?

I presume you mean changing y= 9/x2 into x= 9/y2. Yes, that will "reflect" the graph through the line y= x.
 
  • #3


(1) To graph the equation y = 9 divided by x^2 without using a calculator and besides plotting points, we can use the rules of transformations. The equation y = 9 divided by x^2 can be rewritten as y = 9 * (1/x^2). This allows us to see that the graph will be a reflection of the graph of y = 9 * x^2 about the y-axis.

To graph y = 9 * x^2, we can start with a basic parabola with its vertex at (0,0) and points on either side such as (-1,9) and (1,9). Then, we can reflect these points about the y-axis to get the corresponding points for y = 9 divided by x^2. This will give us a graph that looks like a sideways "U" with its vertex at (0,0) and points on either side such as (-1,1/9) and (1,1/9).

(2) Yes, if we replace x with y and y with x, we can reflect the equation 9/x^2. The resulting equation would be x = 9/y^2. This is because when we reflect a graph about the line y = x, the x and y coordinates switch places. So, the graph of y = 9/x^2 would be the same as the graph of x = 9/y^2, just rotated 90 degrees counterclockwise.
 

Related to How to Graph y = 9/x² Without a Calculator?

1. What is the slope of the graph?

The slope of the graph y = 9 is 0. This is because the equation is a horizontal line with a constant y-value of 9. All points on this line have the same y-coordinate, resulting in a flat slope of 0.

2. What is the y-intercept of the graph?

The y-intercept of the graph y = 9 is 9. This is because the equation represents a horizontal line passing through the y-axis at the point (0,9). The y-intercept is the point where the graph intersects with the y-axis, and for this equation, it will always be 9.

3. What is the domain of the graph?

The domain of the graph y = 9 is all real numbers, or (-∞,∞). This is because the equation has no restrictions on the input values (x) and can take on any real number value. This results in a horizontal line that extends infinitely in both directions along the x-axis.

4. What is the range of the graph?

The range of the graph y = 9 is a single value of 9. This is because the equation has a constant y-value of 9 and therefore, all points on the graph will have a y-coordinate of 9. The range is the set of all possible output values (y) and in this case, it is just the single value of 9.

5. What does the graph of y = 9 look like?

The graph of y = 9 is a horizontal line passing through the point (0,9) and extending infinitely in both directions along the x-axis. It is a straight line with a slope of 0 and a y-intercept of 9. The graph will always be at a constant height of 9, regardless of the x-value.

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