Can someone explain how I can find the range of a function with a prescribed domain.
E.X
f(x) = 2x^2 + 4 for –3 < x < 5. What is the range of f?
f(x) = 1/x for -2 < x < 3 What is the range of f?
Thanks in advance =]!
Can someone explain how I can find the range of a function with a prescribed domain.
E.X
f(x) = 2x^2 + 4 for –3 < x < 5. What is the range of f?
f(x) = 1/x for -2 < x < 3 What is the range of f?
Thanks in advance =]!
Use the minimum and maximum values of your domain and apply them to f(x) to obtain min and max values for your range.
$\displaystyle f(-3)=2(-3)^2+4=22$
$\displaystyle f(5)=2(5)^2+4=54$
The vertex of the parabola is the minimum point of y=4
$\displaystyle y=2x^2+4$
$\displaystyle y=2(x-0)^2+4$
Vertex is at (0, 4)
The range of your first example: $\displaystyle \{y|4<y<54\}$
Hello Ferken,
The function, $\displaystyle f(x) = 2x^2+4$ is an upward parabola whose minimum value is 4 when x = 0.
Here, f(0) = 4
f(-3) = 22
and f(5) = 54
so, Range $\displaystyle = \{f(x)|4<f(x)<54\}$
Please see the attached graph for more clarification.
Now, do the second question in the same way.
Did you get it now ???