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 th
e 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
2 answers:
Answer:
The correct options are:
- A) F(x) is less 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.
- F) F(x) is greater than 0 on the interval 1 is less than x and x is less than 3.
- G) F(x) is less than 0 on the interval x is greater than 3.
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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