The functions f(x) = x2 – 3 and g(x) = –x2 + 2 are shown on the graph.

The graph shows f of x equals x squared minus 3, which is an upward opening parabola with a vertex at 0 comma negative 3 and a point at negative 1 comma negative 2 and a point at 1 comma negative 2. The graph also shows g of x, which is a downward opening parabola with a vertex at 0 comma 2 and a point at negative 1 comma 1 and a point at 1 comma 1.

Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?

y ≤ x2 – 3
y > –x2 + 2

Question

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MrRoyal MrRoyal · Answer 1 · 2022-06-23T19:38:33+02:00

The set of inequalities y ≤ x² - 3 and y > -x² + 2 do not have a solution

The attached figure 1 represents the missing piece in the question

From the graph, we have:

f(x) = x² - 3

g(x) = -x² + 2

Next, we change the equations to inequalities as follows:

y ≤ x² - 3

y > -x² + 2

To modify the graph, we then perform the following transformations:

After the modifications in (a), we have:

y ≤ x² - 3 and y > -x² + 2

Next, we plot the graph of the inequalities

From the graph of the inequalities, the curves of the inequalities have no point of intersection

Hence, the set of inequalities do not have a solution