Question

Follow the steps for graphing a rational function to graph the function R(x) = x²+x-12 If needed, first write the given function as a single rational expression. Then, factor the numerator and denominator of R(x). Select the correct choi choice. A. R(x)- (x + 4)(x-3)

Answer 1

Graphing the quadratic function R(x) = x²+x-12 involves factoring to (x+4)(x-3), finding the x-intercepts, the axis of symmetry, and the y-intercept, then drawing a smooth curve through these points.

Step-by-step explanation:

The function R(x) = x²+x-12 is actually a quadratic function, not a rational function, as it does not have a denominator. This question seems to be confused with the process of graphing rational functions. Instead, let’s focus on graphing the quadratic function provided. To graph the function, we must first factor the quadratic equation.

Factoring the quadratic, we get R(x) = (x+4)(x-3). The solutions to the equation R(x) = 0, also known as the x-intercepts or roots of the equation, are x = -4 and x = 3. Plot these points on the graph. The axis of symmetry can be found by taking the average of the x-intercepts, which in this case is (-4 + 3)/2 = -0.5. The vertex lies on this axis of symmetry and since the coefficient of x² is positive, the parabola opens upwards. You can find the y-intercept by evaluating R(0) which gives us R(0) = -12.

By plotting these points and drawing a smooth curve through them, we can graph the function R(x).