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which of the following statements correctly compares the tow functions f(x) and g(x)?.

Which Of The Following Statements Correctly Compares The Tow Functions Fx And Gx class=
Which Of The Following Statements Correctly Compares The Tow Functions Fx And Gx class=

Sagot :

We have two functions and we have to find which statements are true.

They both have a maximum value of 1.

f(x) has a minimum and not a maximum, so this statement is not true.

The graphs of both functions cross the x-axis at 0.

f(x) does not cross the x-axis, so this statement is not true.

The graphs of both functions cross the y-axis at 1.

This is true for f(x).

For g(x), we have to calculate g(0) to find at which value of y the function cross the y-axis:

[tex]g(0)=-4\cdot0^2+1=0+1=1[/tex]

This statement is true.

Function f(x) has a minimum value of 1 and function g(x) has a maximum value of 1.

This is true for f(x).

For g(x), the maximum value happens when x=0, because for all other values of x, the quadratic term becomes more negative.

In the previous statement we calculate g(0)=1, so 1 is the maximum value of g(x).

This statement is true.

They both have a minimum value of 1.

g(x) does not have a minimum value. This statement is not true.

Answer: The statement that are true:

- The graphs of both functions cross the y-axis at 1.

- Function f(x) has a minimum value of 1 and function g(x) has a maximum value of 1.