Question

suppose a function $f$ is continuous on $0,1$, except at $x = 0.25$ and that $f(0)=1$ and $f(1)=3$. is it necessarily true that the conclusion to the intermediate value theorem will hold? answer \y\ for yes or
\ for no below.

Explanation:

Step1: Recall Intermediate Value Theorem

The Intermediate - Value Theorem states that if a function $y = f(x)$ is continuous on a closed interval $[a,b]$, and $k$ is a number between $f(a)$ and $f(b)$, then there exists at least one number $c$ in the interval $(a,b)$ such that $f(c)=k$.

Step2: Analyze given function

The function $f$ is not continuous on the closed interval $[0,1]$ since it is discontinuous at $x = 0.25$. The conditions for the Intermediate - Value Theorem are not met. For example, there could be a jump or a break at $x=0.25$ that prevents the function from taking on certain values between $f(0)=1$ and $f(1)=3$.

Answer:

n