Question

Finding x-Intercepts Algebraically Jan 04, 2:10:40 PM Watch help video Find all x-intercept s of the following function. Write your answer or answers as coordinate points. Be sure to select the appropriate number of x-intercept s. f(x)=(9x²-16)/(x²+6x)

Answer 1

To find the x-intercepts of the function f(x) = (9x²-16)/(x²+6x), set the numerator equal to zero and solve. The x-intercepts are (4/3, 0) and (-4/3, 0).

Step-by-step explanation:

To find the x-intercepts of the function f(x) = (9x²-16)/(x²+6x), we need to set the function equal to zero and solve for x. We do this by setting the numerator equal to zero: 9x² - 16 = 0. Next, we factor the quadratic equation by recognizing that it is a difference of squares: (3x - 4)(3x + 4) = 0. Setting each factor equal to zero gives us two solutions: 3x - 4 = 0 and 3x + 4 = 0. Solving for x in each equation, we get x = 4/3 and x = -4/3. Therefore, the x-intercepts of the function are (4/3, 0) and (-4/3, 0).