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This is a graphing problem and I am trying to find the x-intercepts and the y-intercepts. Please show me the full steps. I really appreciate it thank you.

This is a graphing problem and I am trying to find the x-intercepts and the y-intercepts-example-1
User Chat
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Answer:

  • y-intercept: y = 3/4
  • no x-intercepts

Explanation:

To find the y-intercept, set x=0 and evaluate the function.

f(0) = -3/(0 -4) = 3/4

The y-intercept is (0, 3/4).

__

To find the x-intercept(s), set f(x) = 0 and solve for x.

0 = -3/(x^2 -4)

0 = -3 . . . . . . . . . . multiply by (x^2 -4), x ≠ ±2

There are no values of x that will make this true. There are no x-intercepts.

_____

Additional comments

In general, you find the x-intercepts of a rational function by finding the zeros of the numerator. Here, the numerator is -3, so cannot ever be zero.

I find a graphing calculator to be a useful tool for showing where to look for x-and y-intercepts. The attached graph shows y=0 (the x-axis) is a horizontal asymptote, so there are no x-intercepts.

This is a graphing problem and I am trying to find the x-intercepts and the y-intercepts-example-1
User Stefan Ferstl
by
8.2k points

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