Final answer:
The y-intercept of the function g(x) occurs at the point (0, 2) and the x-intercept occurs at the point (-3, 0).
Step-by-step explanation:
To determine the x-intercept and y-intercept of the given function g(x)=(2x+6)/(-6x+3), we follow the standard procedure for finding intercepts:
- For the y-intercept, we set x to 0 and solve for g(x), which gives us the value of y where the graph intersects the y-axis.
- For the x-intercept, we set g(x) to 0 and solve for x, which gives us the value(s) of x where the graph intersects the x-axis.
Let's find the y-intercept:
Set x = 0 in g(x), we get g(0) = (2(0)+6)/(-6(0)+3) = 6/3 = 2. Therefore, the y-intercept is at the point (0, 2).
Now, let's find the x-intercept:
Set g(x) = 0, we get 0 = (2x+6)/(-6x+3), which implies that 2x + 6 = 0 since the denominator can not be equal to 0 (as it would make the fraction undefined). Solving for x gives us x = -6/2 = -3. Hence, the x-intercept is at the point (-3, 0).