Makakuha ng detalyadong mga sagot sa lahat ng iyong tanong sa IDNStudy.com. Makakuha ng mga sagot sa iyong mga tanong mula sa aming mga eksperto, handang magbigay ng mabilis at tiyak na solusyon.
Answer:
1. Start with the basic function: The function ( y = x² ) represents a parabola that opens upwards with its vertex at (0, 0).
2. Shift the function: The given function is ( y = x² + 1 ), which means the entire parabola is shifted 1 unit up. Therefore, its vertex is now at (0, 1).
3. Determine the minimum value: The minimum value of ( y = x² + 1 ) occurs at the vertex of the parabola. Since ( x² ) is always non-negative
[tex](i.e., ( x^2 \geq 0 ))[/tex]
the smallest value of ( y ) is:
[tex]y_{\text{min}} = 0 + 1 = 1[/tex]
4. Determine the range: As ( x ) increases or decreases without bound, ( x² ) becomes very large, and so does ( y ). Therefore, ( y ) can take any value greater than or equal to 1.
The range of the function ( y = x² + 1 ) is:
[tex] \:\boxed{[1, \infty)}[/tex]
This means ( y ) can be any value starting from 1 and increasing to infinity.
Step-by-step explanation:
Pa Click Brainliest me Thank you.