Questions: Suppose that f and g are functions graphed as shown. The red graph is the graph of y=f(x) and the blue is y=g(x). Based on the graph, find the set of all x-values for which f(x) ≥ g(x). Enter your answer using interval notation.

Suppose that f and g are functions graphed as shown. The red graph is the graph of y=f(x) and the blue is y=g(x). Based on the graph, find the set of all x-values for which f(x) ≥ g(x). Enter your answer using interval notation.

Transcript text: Suppose that $f$ and $g$ are functions graphed as shown. The red graph is the graph of $y=f(x)$ and the blue is $y=g(x)$. Based on the graph, find the set of all $x$-values for which $f(x) \geq g(x)$. Enter your answer using interval notation.

Solution

Solution Steps

Step 1: Identify the Intersection Points

First, identify the points where the red graph $ y = f(x) $ intersects the blue graph $ y = g(x) $. These points are where $ f(x) = g(x) $.

From the graph, the intersection points are approximately at:

$ x = -3 $
$ x = -1 $
$ x = 2 $

Step 2: Determine the Intervals

Next, determine the intervals between these intersection points:

$ (-\infty, -3) $
$ (-3, -1) $
$ (-1, 2) $
$ (2, \infty) $

Step 3: Test Each Interval

Test each interval to see where $ f(x) \geq g(x) $:

For $ x \in (-\infty, -3) $, $ f(x) $ (red) is below $ g(x) $ (blue), so $ f(x) < g(x) $.
For $ x \in (-3, -1) $, $ f(x) $ (red) is above $ g(x) $ (blue), so $ f(x) \geq g(x) $.
For $ x \in (-1, 2) $, $ f(x) $ (red) is below $ g(x) $ (blue), so $ f(x) < g(x) $.
For $ x \in (2, \infty) $, $ f(x) $ (red) is below $ g(x) $ (blue), so $ f(x) < g(x) $.