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To find the intercepts of the function f(x) = (x-3)/(x^2 + 2x -3), we need to find the x-intercept and the y-intercept. 1. X-intercept: The x-intercept is the value of x when f(x) = 0. So, we set the function equal to zero and solve for x. 0 = (x-3)/(x^2 + 2x -3) This implies that the numerator of the fraction must be zero (since zero times anything is zero). So, we set x - 3 = 0 and solve for x. x - 3 = 0 x = 3 So, the x-intercept is 3. 2. Y-intercept: The y-intercept is the value of f(x) when x = 0. So, we substitute x = 0 into the function and solve for f(x). f(0) = (0-3)/(0^2 + 2*0 -3) = -3/-3 = 1 So, the y-intercept is 1. Therefore, the intercepts of the function are x = 3 and y = 1. Context: this is mcq a) (2,0) b) (3,0) C) (1,0)

Question

To find the intercepts of the function f(x) = (x-3)/(x^2 + 2x -3), we need to find the x-intercept and the y-intercept.

  1. X-intercept: The x-intercept is the value of x when f(x) = 0. So, we set the function equal to zero and solve for x.

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

    This implies that the numerator of the fraction must be zero (since zero times anything is zero). So, we set x - 3 = 0 and solve for x.

    x - 3 = 0 x = 3

    So, the x-intercept is 3.

  2. Y-intercept: The y-intercept is the value of f(x) when x = 0. So, we substitute x = 0 into the function and solve for f(x).

    f(0) = (0-3)/(0^2 + 2*0 -3) = -3/-3 = 1

    So, the y-intercept is 1.

Therefore, the intercepts of the function are x = 3 and y = 1. Context: this is mcq a) (2,0) b) (3,0) C) (1,0)

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Solution

The correct answer is b) (3,0).

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