Question

For the rational function f(x)=x-2/3x^2+x-2, fill in the points on the graph at the function value f(x)=2.

Answer 1

(-2/3, 2), (1/2, 2)

Explanation:

A graphing calculator can show you those points: (-2/3, 2), (1/2, 2).

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Put the given value in the equation and solve for x.

2 = f(x)

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

2(3x^2 +x -2) -(x -2) = 0 . . . . . multiply by the denominator; put in standard form

6x^2 +x -2 = 0 . . . . . collect terms

(3x +2)(2x -1) = 0 . . . factor

Solutions are values of x that make the factors zero:

x = -2/3, x = 1/2

Then the points on the graph are (-2/3, 2) and (1/2, 2).