━What are the x-intercepts of the function below? g(x)=(2x−3)(x−6) (1 point) Responses (3, 0) and (6, 0) (3, 0) and (6, 0) (-1.5, 0) and (-6, 0) (-1.5, 0) and (-6, 0) (1.5, 0) and (6, 0) (1.5, 0) and (6, 0) (-3, 0) and (-6, 0)
The x-intercepts of a function occur when the value of y is equal to zero. To find the x-intercepts of g(x)=(2x−3)(x−6), we set y=0 and solve for x:
0 = (2x−3)(x−6)
This equation will be true when either 2x-3 = 0 or x-6 = 0. Solving for x in each case:
2x - 3 = 0
2x = 3
x = 3/2 = 1.5
x - 6 = 0
x = 6
Therefore, the x-intercepts are (1.5, 0) and (6, 0).
The answer is: (1.5, 0) and (6, 0)