Respuesta :
The range of the given piecewise function is [-1, 27].
A function with many parts of curves in its graph is said to be a piecewise function. It is a function with various definitions at various intervals of x.
The given function is a piecewise function,
[tex]f(x)=\begin{cases}{{x^2+2\;&\text{if}\;-5\le x < 3 \\{x-4\;&\text{if}\;3\le x < 7}}\end{cases}[/tex]
From the given function,
- f(x) = x²+2 if the x value is less than or equal to -5 and less than 3.
- f(x) = x-4 if the x value is less than or equal to 3 and less than 7.
The set of values for all the output values can be referred to as a function's range. To find a range,
- For the domain -5 ≤ x < 3, the function is f(x) = x²+2. Substitute x = -5 in this function, and we get f(x) = 27.
- For domain 3 ≤ x < 7, the function is f(x) = x-4. Substitute x = 3 in this function, and we get f(x) = -1.
Then, the range can be written as [-1, 27]. Therefore, the first option is correct.
The complete question is -
Find the range of the following piecewise function.
[tex]f(x)=\begin{cases}{{x^2+2\;&\text{if}\;-5\le x < 3 \\{x-4\;&\text{if}\;3\le x < 7}}\end{cases}[/tex]
a) [-1,27] b) [18,-2] c) [1,27] d) [-4,0].
To know more about the range:
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