Answer:
To find the domain of the function f(x) = 4x + 7 on the given interval [-6, 0], we need to determine the set of all possible x-values within that interval.
Since the interval is [-6, 0], the domain will consist of all x-values between -6 and 0, including -6 and 0. So, the domain in interval notation is [-6, 0].
To find the range of the function, we need to determine the set of all possible y-values or output values. Since f(x) = 4x + 7 is a linear function that increases as x increases, the range will extend from the minimum value to the maximum value within the given interval.
To find the minimum and maximum values of f(c) on the given interval, we evaluate the function at the endpoints of the interval.
When x = -6:
f(-6) = 4(-6) + 7
f(-6) = -24 + 7
f(-6) = -17
When x = 0:
f(0) = 4(0) + 7
f(0) = 0 + 7
f(0) = 7
Therefore, the minimum value of f(c) on the given interval is -17, and the maximum value is 7.
Finally, the intercepts can be found by setting f(x) = 0 and solving for x:
When f(x) = 0:
4x + 7 = 0
4x = -7
x = -7/4
So, the x-intercept is (-7/4, 0).
Similarly, to find the y-intercept, we set x = 0:
f(0) = 4(0) + 7
f(0) = 0 + 7
f(0) = 7
Therefore, the y-intercept is (0, 7).
In summary:
- The domain in interval notation is [-6, 0].
- The range extends from the minimum value -17 to the maximum value 7.
- The x-intercept is (-7/4, 0).
- The y-intercept is (0, 7).