Question

1. a) on what intervals of x is f(x) positive?

b) on what intervals of x does f(x) have a positive slope?
c) on what intervals of x is f(x) increasing?

1. a) on what intervals of x does f(x) have a positive slope?

b) on what interval of x is f(x) negative?

Explanation:

Problem 3

Step1: Analyze f(x) positive regions

Identify where the graph is above the x-axis.
The graph is above the x-axis when $x > 0$.

Step2: Analyze positive slope regions

Identify where the graph rises left to right.
The graph has a positive slope when $-2 < x < 2$.

Step3: Analyze increasing regions

Increasing means positive slope (rising left to right).
The graph is increasing when $-2 < x < 2$.

Step1: Analyze positive slope regions

Identify where the parabola rises left to right.
The parabola opens upward, so it rises when $x > 1$.

Step2: Analyze f(x) negative regions

Identify where the graph is below the x-axis.
The graph is below the x-axis between its two x-intercepts, $-1 < x < 3$.

Answer:

a) $x > 0$ or $(0, \infty)$
b) $-2 < x < 2$ or $(-2, 2)$
c) $-2 < x < 2$ or $(-2, 2)$

---

Problem 4