The range of f(x) = |x| is y ≥ 0. If a < 0 and b ≠ 0 for g(x) = a|x| + b, what is the range of function g?

Step-by-step explanation: Finding the range of a function y=f (x)is the same as finding all values that y could be. To do this, we can think of it this way: The range of f(x) is all the y-values where there is a number x with y=f (x).We can try and motivate how to find this with an example. Let's try to find the range of: f(x) =x2+1 So we want to find y-values such that there is some x where y=x2+1. Suppose we want to check if y=5 is in the range of f(x).Then, we want to check if there is an x-value such that x2+1=5. We can solve this equation as follows:2+1 5x2=4x=±2 So since either x=2 or x=−2 works, we know that y=5 is in the range of f(x).More generally, if we want to find the full range of y=x2+1, we can solve for x (taking the inverse of the function) to get x=√y−1. Then, the range of f(x) is simply the domain of √y−1, because these are all the values where there is some x-value with f(x)=y. In this example, the domain of √y−1 is just all values where y−1≥0, so [1,∞ is the range of f(x)=x2+1.Overall, the steps for algebraically finding the range of a function are: Write down y=f(x) and then solve the equation for x, giving something of the form x=g(y).Find the domain of g(y), and this will be the range of f(x).If you can't seem to solve for x, then try graphing the function to find the range.

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