The function f(x) = -x^2 + 4x - 3 is graphed in the xy-coordinate plane as shown. based on the graph of the function which of the following statements are true? select all that apply. a. f(x) is less than 0 on the interval x is less than 0 b. f(x) is greater than 0 on the interval x is less than 0 c. f(x) is less than 0 on the interval 0 is less than x and x is less than 1 d. f(x) is greater than 0 on the interval 0 is less than x and x is less than 1 e. f(x) is less than 0 on the interval 1 is less than x and x is less than 3 f. f(x) is greater than 0 on the interval 1 is less than x and x is pess than 3 g. f(x) is less than 0 on the interval x is greater than 3 h. f(x) is greater than 0 on the interval x is greater than 3

The correct options are:

Step-by-Step explanation:

We are given a function f(x) as:

This function f(x) could also be written as:

Now we will do each of the options:

A)

when x<0

then (1-x)>0 and (x-3)<0

Hence,

F(x)<0.

it could also be seen in the graph.

Hence, option A is correct.

B)

option: B is the opposite of option A and hence is false.

C)

In the interval 0<x<1.

we see that the graph of the function F(x) lie below the x-axis.

Hence, F(x) <0

Hence, option: C is correct.

D)

option: D is opposite of option C and hence is false.

E)

Clearly from the graph we could observe that:

F(x)>0 in the interval 1<x<3.

Hence, option E is incorrect.

F)

Option: F is opposite of option: E and hence is true.

G)

Again in the interval x>3 the graph of the function is below x-axis.

and hence F(x)<0 in the interval x>3.

Hence, option: G is correct.

H)

option: H is false.

since F(x)<0 in the interval x>3.

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step-by-step explanation: