Question
What are the key aspects of the graph of f(x) = x2 – b2, where b is a real number?
Answers
Answered by
GPT 3.5
1. The graph of f(x) = x^2 - b^2 is a parabola with the vertex at the origin (0, 0).
2. The parabola opens upwards if b is positive and downwards if b is negative.
3. The value of b affects the width of the parabola. A larger value of b will result in a wider parabola.
4. The graph intersects the x-axis at x = b and x = -b.
5. The graph is symmetric with respect to the y-axis, as f(x) = f(-x) for all real numbers x.
6. The minimum value of the function f(x) is -b^2, which occurs at x = 0.
2. The parabola opens upwards if b is positive and downwards if b is negative.
3. The value of b affects the width of the parabola. A larger value of b will result in a wider parabola.
4. The graph intersects the x-axis at x = b and x = -b.
5. The graph is symmetric with respect to the y-axis, as f(x) = f(-x) for all real numbers x.
6. The minimum value of the function f(x) is -b^2, which occurs at x = 0.