Question

Given the piecewise function shown below, select all of the statements that are true. (includes pic)

thanks

Answer 1

A and C

Explanation:

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

Given piecewise function:

`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}`

Therefore, the function has three definitions:

• 
  `\textsf{If $x$ is less than $1$ then $f(x) = 2x$}.`
• 
  `\textsf{If $x$ equals $1$ then $f(x) = 5$}.`
• 
  `\textsf{If $x$ is greater than $1$ then $f(x) = x^2$}.`

`\textsf{A.} \quad f(1) =5`

This statement is true as when x = 1, f(x) = 5.

`\textsf{B.} \quad f(5)=1`

This statement is false as when x is greater than 1, f(x) = x²:

`\implies f(5)=(5)^2=25`

`\textsf{C.} \quad f(2)=4`

This statement is true as when x is greater than 1, f(x) = x²:

`\implies f(2)=(2)^2=4`

`\textsf{D.} \quad f(-2)=4`

This statement is false as when x is less than 1, f(x) = 2x:

`\implies f(-2)=2(-2)=-4`