The functions f(x) = x^2 – 2 and g(x) = –x^2 + 5 are shown on the graph.

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 > x^2 – 2
y ≥ –x^2 + 5

The relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal. But to compare the values, whether it is less than or greater than, different inequalities are used.

Given:

f(x)= x²-2

g(x) = -x²+5

To derive, y ≤ x² + 5 simply change the equality sign in the function g(x).

To derive y > x² - 2 , following transformation on the function f(x)

Shift the function f(x) down by 2 units
Reflect across the x-axis
Shift the function g(x) up by 5 units
Change the equality sign in the function g(x) to greater than.

The inequalities of the graphs become

y < x² - 2 and y ≤ x² - 5

From the graph of the above inequalities it can be seen that curves of the inequalities do not intersect.

Hence, the set of inequalities do not have a solution

Learn more about inequalities here:

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The functions f(x) = x^2 – 2 and g(x) = –x^2 + 5 are shown on the graph. 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 > x^2 – 2 y ≥ –x^2 + 5

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What is inequality?

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The functions f(x) = x^2 – 2 and g(x) = –x^2 + 5 are shown on the graph.

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 > x^2 – 2
y ≥ –x^2 + 5