Question

Please help me! Please no guesses and explain how you got the answer. I've reviewed the lesson but I don't understand the question and the lesson doesn't clear up anything.

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

The graph shows f of x equals x squared minus 1, which is an upward opening parabola with a vertex at 0 comma negative 1 and a point at negative 1 comma 0 and a point at 1 comma 0. The graph also shows g of x, which is a downward opening parabola with a vertex at 0 comma 4 and a point at negative 1 comma 3 and a point at 1 comma 3.

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

Answer 1

We will need to shade the region above f(x) and the region below the function g(x).

How to transform the graph into the solution set?

We have:

f(x) = x^2 - 1

g(x) = -x^2 + 4

Both of these are already graphed, and we want to transform it into:

y > f(x)

y ≤ g(x)

The first inequality means that we need to graph f(x) with a dashed line, because f(x) is not part of the solution, and then we shade all the region above f(x).

For the other inequality, we use a solid line (because the points on the line are solutions) and then we shade the part below the curve.