Question

Consider the inverse function. Which conclusions can be drawn about f(x) = x2 + 2? Select three options. f(x) has a limited range. f(x) has a restricted domain. f(x) has an x-intercept of (2, 0). f(x) has a maximum at the point (0, 2). f(x) has a y-intercept at the point (0, 2).

Answer 1

The conclusions that can be drawn about
`f(x) = x^2 + 2` are: it has a restricted domain, it has a y-intercept at (0, 2), and it has a maximum at (0, 2).

Step-by-step explanation:

The function
`f(x) = x^2 + 2` is a quadratic function that represents a parabola. Based on the given options, the correct conclusions that can be drawn are:

1. f(x) has a restricted domain: The function is defined for all real numbers because there are no restrictions on the value of x.
2. f(x) has an x-intercept of (2, 0): To find the x-intercept, set f(x) equal to 0 and solve for x. In this case,
   `x^2 + 2 = 0,` which has the solution x = ±√(-2). Since the square root of a negative number is undefined, there are no real x-intercepts, so this option is incorrect.
3. f(x) has a y-intercept at the point (0, 2): To find the y-intercept, substitute x = 0 into the function. In this case, f(0) =
   `0^2 + 2 = 2`, so the y-intercept is (0, 2).
4. f(x) has a maximum at the point (0, 2): To determine if f(x) has a maximum or minimum, we can check the coefficient of the
   `x^2`term. Since this coefficient is positive, the parabola opens upwards, and the vertex represents the maximum point. In this case, the vertex is at (0, 2).

Answer 2

A,B,E

Step-by-step explanation:

2021 Edgenutity. Algebraric reasoning B