Answer:
Domain: set of all real numbers
Range: [tex]y \geq -5[/tex]
Step-by-step explanation:
We have to find the domain and range of the function:
[tex]f(x) =5x^2+10x[/tex]
This is a quadratic function, shape of a "U", that's called a parabola.
The domain is the set of x values for which the function is defined.
The range is the set of y values for which the function is defined.
Normally, any parabola in the form [tex]ax^2+bx+c[/tex] has domain as "all real numbers". This is the case for this problem as well, thus,
Domain = set of all real numbers
Now, for the range, we have to look at the minimum value of the function. So, the range would be y values greater than or equal to the minimum number. Lets find the minimum value of this function.
We have to find the value of x for which the minimum occurs by using the formula:
[tex]x=\frac{-b}{2a} =\frac{-10}{2(5)} =-1[/tex]
Note: value of a is "5" and b is "10"
Now, we plug this into the function to find the minimum value:
[tex]f(x)=5x^2+10x\\f(-1)=5(-1)^2 +10(-1)\\f(-1)=-5[/tex]
So, the range is set of all real numbers greater than or equal to -5.
