The functions f(x) = x2 – 1 and g(x) = –x2 + 4 are shown on the graph.

20pts
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 – 1
y ≤ –x2 + 4

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The equation of the function f(x) = x² - 1

The equation of the function g(x) = -x² + 4

Let f(x) is the parent function.

To get the equation of the function g(x):

Applying transformation to function f(x)

f(x) → f(x) + 5 (function will shift up side by 5 units)

F(x) = x² - 1 + 5

F(x) = x² + 4

F(x) → -x² (funtion will reflect about the line y = 4)

g(x) = -x² + 4

Thus, the equation of the function g(x) is g(x) = -x² + 4 after applying the transformation.

Learn more about the function here:

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The functions f(x) = x2 – 1 and g(x) = –x2 + 4 are shown on the graph. 20pts 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 – 1 y ≤ –x2 + 4

Respuesta :

What is a function?

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The functions f(x) = x2 – 1 and g(x) = –x2 + 4 are shown on the graph.

20pts
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 – 1
y ≤ –x2 + 4