Question

PLEASE HELP

Choose between ones that are slashed

ex: the grass is red/green

choose the one that's correct

You have to/do not have to restrict the domains of quadratic functions and absolute value functions, because these functions are one-to-one/many-to-one functions. For instance, the quadratic function f(x) = x^2 pairs both −2 and 2 with 4, and the absolute value function f(x) = |x| pairs both −2 and 2 with 2.

Linear functions (excluding constant functions) and exponential functions are one-to-one/many-to-one functions, so their domains do/do not to be restricted.

Answer 1

restrict the domains of quadratic functions and absolute value functions, because these functions are functions. For instance, the quadratic function f(x) = x^2 pairs both −2 and 2 with 4, and the absolute value function f(x) = |x| pairs both −2 and 2 with 2.

Explanation:

Answer 2

`\textbf{You have to}` restrict the domains of quadratic functions and absolute value functions, because these functions are
`\textbf{many-to-one}` functions. For instance, the quadratic function f(x) = x^2 pairs both −2 and 2 with 4, and the absolute value function f(x) = |x| pairs both −2 and 2 with 2.

Linear functions (excluding constant functions) and exponential functions are
`\textbf{one-to-one}` functions, so their domains
`\textbf{do not need}` to be restricted.
_________________

An absolute value function, without domain restriction, has an inverse that is NOT a function.

In order to guarantee that the inverse must also be a function, we need to restrict the domain of the absolute value function to make it a one-to-one function.