Answer:
A and C
Step-by-step explanation:
Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.
Given piecewise function:
[tex]f(x)=\begin{cases}2x \quad &\text{if }x < 1\\5 \quad &\text{if }x=1\\x^2 \quad &\text{if }x > 1\end{cases}[/tex]
Therefore, the function has three definitions:
- [tex]\textsf{If $x$ is less than $1$ then $f(x) = 2x$}.[/tex]
- [tex]\textsf{If $x$ equals $1$ then $f(x) = 5$}.[/tex]
- [tex]\textsf{If $x$ is greater than $1$ then $f(x) = x^2$}.[/tex]
[tex]\textsf{A.} \quad f(1) =5[/tex]
This statement is true as when x = 1, f(x) = 5.
[tex]\textsf{B.} \quad f(5)=1[/tex]
This statement is false as when x is greater than 1, f(x) = x²:
[tex]\implies f(5)=(5)^2=25[/tex]
[tex]\textsf{C.} \quad f(2)=4[/tex]
This statement is true as when x is greater than 1, f(x) = x²:
[tex]\implies f(2)=(2)^2=4[/tex]
[tex]\textsf{D.} \quad f(-2)=4[/tex]
This statement is false as when x is less than 1, f(x) = 2x:
[tex]\implies f(-2)=2(-2)=-4[/tex]
