The y-intercept of a function is the point where x = 0.
The ordered pair that represents the greatest y-intercept is (0,3)
The functions are given as:
[tex]\mathbf{f(x) = |x - 1| + 2}[/tex]
[tex]\mathbf{g(x) = (x + 3)}[/tex]
[tex]\mathbf{h(x) = (x + 1) - 3}[/tex]
Set x = 0, and solve the functions
[tex]\mathbf{f(x) = |x - 1| + 2}[/tex]
Substitute 0 for x
[tex]\mathbf{f(0) = |0 - 1| + 2}[/tex]
[tex]\mathbf{f(0) = |- 1| + 2}[/tex]
Remove absolute brackets
[tex]\mathbf{f(0) = 1 + 2}[/tex]
[tex]\mathbf{f(0) = 3}[/tex]
[tex]\mathbf{g(x) = (x + 3)}[/tex]
Substitute 0 for x
[tex]\mathbf{g(0) = (0 + 3)}[/tex]
[tex]\mathbf{g(0) = 3}[/tex]
[tex]\mathbf{h(x) = (x + 1) - 3}[/tex]
Substitute 0 for x
[tex]\mathbf{h(0) = (0 + 1) - 3}[/tex]
[tex]\mathbf{h(0) = 1 - 3}[/tex]
[tex]\mathbf{h(0) = - 2}[/tex]
Hence, the ordered pair that represents the greatest y-intercept is (0,3)
Read more about ordered pairs at:
https://brainly.com/question/3309631
