Final answer:
To evaluate the piecewise function, use the appropriate part of the definition based on whether the input is less than or greater than 0. For f(-5), use f(x) = x² + 1 to get 26, for f(0), use f(x) = x to get 0, and for f(1), also use f(x) = x to get 1.
Step-by-step explanation:
The question asks to evaluate f(-5), f(0), and f(1) for a piecewise defined function given by:
For x less than 0: f(x) = x² + 1
For x greater than or equal to 0: f(x) = x
Evaluating f(-5): Since -5 is less than 0, we use the first part of the function definition.
f(-5) = (-5)² + 1 = 25 + 1 = 26
Evaluating f(0): 0 is equal to 0, so we use the second part of the function definition.
f(0) = 0 = 0
Evaluating f(1): Since 1 is greater than 0, we again use the second part of the function definition.
f(1) = 1 = 1
�(−5)=26,�(0)=0,�(1)=1
f(−5)=26,f(0)=0,f(1)=1
So, �(−5)=26
f(−5)=26, �(0)=0
f(0)=0, and �(1)=1
f(1)=1 are the correct evaluations for the given piecewise defined function. The function switches behavior at
�=0x=0, providing different expressions for
�<0x<0 and �≥0x≥0.