Answer:
a. The domain of the function is -3 < x ≤ 5
b. The range of the function is -3 ≤ y < 3
c. The y-intercept is the point (0, 0)
d. The values of 'x' at which f(x) ≥ 0 are;
x = -3, x = 1, x = 5
e. The intervals over which f(x) is decreasing are;
-3 < x ≤ - 1, and 1 ≤ x ≤ 3,
f. The local minimums are;
(-1, -1), and (3, -3)
Step-by-step explanation:
a. The domain of a function is the set of the possible independent variable values
Therefore, the domain of the function is -3 < x ≤ 5
b. The range of a function is the set of the possible values of the dependent variable
Therefore, the range of the function is -3 ≤ y < 3
c. The y-intercept is the point (0, 0)
d. The values of 'x' for which f(x) ≥ 0 are;
x = -3, x = 1, x = 5
The range of values of 'x' where f(x) ≥ 0 are;
-3 < x ≤ - 1.5, 0 ≤ x ≤ 1.5, 4.5 ≤ x ≤ 5
e. f(x) is decreasing over the following intervals;
-3 < x ≤ - 1, and 1 ≤ x ≤ 3,
f. The local minimums are the points that are lowest compared to other nearby points
The local minimums are;
(-1, -1), and (3, -3).
