Let's get the terminology straight. You expanded (x-3)2 ; it was already factored.Codester09 said:Homework Statement
Find the range of h
Homework Equations
h(x) = sqrt(25 + (x - 3)2)
The Attempt at a Solution
I factored out the (x-3)2 and simplified to get
sqrt(x2 - 6x + 34)
The best thing, IMO, was to leave the radicand in its given form, 25 + (x-3)2. Looking at that as its own function, what is the range of this function? That will tell you a lot about the range of h(x).Codester09 said:I was trying to figure out the domain first, knowing that x2 - 6x >= -34 in order for the number inside the sqrt to be non-negative.. I don't know, maybe I'm missing something really basic here. Help? :)
The range of a function refers to the set of all possible output values or y-values that a function can produce.
To find the range of a function, you can graph the function and observe the y-values or output values. Alternatively, you can also use algebraic methods such as substitution or factoring to determine the range.
The range of a function is important because it helps to understand the behavior and limitations of a function. It can also help in solving real-world problems and making predictions.
Yes, the range of a function can be infinite if the function continues indefinitely in one direction and never repeats a y-value. This is often the case for exponential and logarithmic functions.
If a function is given in equation form, you can look at the degree of the polynomial or the exponent of the function to determine if the range is finite or infinite. If the degree or exponent is odd, the range is typically infinite. If it is even, the range is usually finite. If the function is given in graph form, you can observe the behavior of the graph to determine the range.