Question

Consider the following graph of a quadratic function. Which of the statements are true? Select all that apply.

A. The function is decreasing over the interval x<-1

B. The range of the function is all real numbers.

C. The function is increasing over the interval x<-1

D. The domain of the function is all real numbers

E. The function has a relative minimum at (-1,5)

Answer 1

C,D,E

Explanation:

Answer 2

Option C,D and E are correct.

Explanation:

Clearly from the graph we could say that it is a graph of a quadratic function.so we will work on each of the following options:

A)

Clearly from the graph we could see that the graph is increasing on both the sides of -1.

Hence, option A is wrong. ( The function is decreasing over the interval x<-1).

B)

As the function is a quadratic function hence the range contains all the real numbers greater than or equal to 5 below 5 it won't take any value.

Hence option B is wrong.(The range of the function is all real numbers).

C)

clearly we could see that the function is increasing in the interval x<-1.

Hence, option C is correct.

D)

The function is defined for all of the real numbers.

Hence option D is correct. (The domain of the function is all real numbers).

E)

Clearly from the graph we could see that the function has minimum value at -1 and the graph is increasing before and after that.

Hence, option E is correct.( The function has a relative minimum at (-1,5) ).