Which are characteristics of the graph of the function f(x) = (x + 1)2 + 2? Check all that apply
The domain is all real numbers,
The range is all real numbers greater than or equal to 1
The y-intercept is 3.
The graph of the function is 1 unit up and 2 units to the Daft from the graph of y = x2
The graph has two x-intercepts

The domain is all real numbers

The y-intercept is 3.

Step-by-step explanation:

Let's analyze each statement separately. The function is

We have the following statements:

The domain is all real numbers, --> TRUE. The domain of a function is the set of values that the variable x can take. For this function, there are no restriction on the values that x can take, so the domain is all real numbers.

The range is all real numbers greater than or equal to 1  --> FALSE. The range of a function is the set of values that the variable y can take. For this function, we see that the factor is always equal or greater than zero; this means that the minimum of the function is , so the range is all real numbers greater than or equal to 2.

The y-intercept is 3.  --> TRUE. The y-intercept is the value of the function when x = 0. For this function, if we substitute x = 0, we find:

The graph of the function is 1 unit up and 2 units to the left from the graph of --> FALSE. The graph of a function is scaled n units up when ; in this case, we see that the factor n in our fuction is n = 2, so the function is actually scaled 2 units up, not 1.

The graph has two x-intercepts --> FALSE. The x-intercept of a graph is the value of x when . If we require for our function, we get:

However, this equation has no solutions: so, the graph has no x-intercepts.

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step-by-step explanation: