Question

You want to restrict the domain of the function shown in the graph below to make it one-to-one so that it will have an inverse. What domain, in interval notation, could you use?

Select all correct answers.

A coordinate plane has a horizontal x-axis labeled from negative 2 to 8 in increments of 1 and a vertical y-axis labeled from negative 1 to 7 in increments of 1. A parabola that opens upward has vertex left-parenthesis 3 comma 1 right-parenthesis and passes through the points left-parenthesis negative 1 comma 7 right-parenthesis and left-parenthesis 7 comma 7 right-parenthesis.

Select all that apply:

• [2,5]

• [3,7]

• [1,6]

• [1,4]

• [−1,3]

• [0,7]

Answer 1

A one to one function should not have two values in domain which map to same value in range .

a parabola has a symetry about vertex . a x value equal distance left to vertex and right to vertex will map to same value in range . so this is not one to one . we need to restrict domain tomake it into one to one.

this is done by restricting x values from left side upto x cordinate of vertex or from x cordinate of vertex to x cordinate of right end side .

here vertex is at (3,1) . so x cordinate is 3 .

left end is at (-1,7) . so x cordinate of left end side is -1

right end is (7,7) . so x cordinate of right end side is 7 .

so two domain for restriction are [-1,3] and [3,7]

so answer are

[-1,3]

[3,7]