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.
