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The functions f(x) = x^2 – 3 and g(x) = –x^2 + 2 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 – 3
y > –x^2 + 2

The functions fx x2 3 and gx x2 2 are shown on the graph Explain how to modify the graphs of fx and gx to graph the solution set to the following system of ineq class=

Respuesta :

MrRoyal

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

How to modify the graphs

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:

  • Shift the function g(x) down by 2 units
  • Reflect across the x-axis
  • Shift the function g(x) down by 3 units

How to identify the solution set

After the modifications in (a), we have:

y ≤ x² - 3 and y > -x² + 2

Substitute y > -x² + 2 in y ≤ x² - 3

-x² - 2 ≤ x² - 3

This gives

2x² ≤ - 1

Divide by 2

x² ≤ - 0.5

The square root of numbers less than 0 is a complex number

Hence, the set of inequalities do not have a solution

Read more about inequalities at:

brainly.com/question/24372553

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