Question

consider the following piece - wise - defined function. $f(x)=\begin{cases}\frac{3}{4}x - 3&\text{if }xlt4\\x + 5&\text{if }xgeq4end{cases}$ step 3 of 3: evaluate this function at $x = 1$. express your answer as an integer or simplified fraction. if the function is undefined at the given value, indicate \undefined\. answer selecting a radio button will replace the entered answer value(s) with the radio button value. if the radio button is not selected, the entered answer is used. $f(1)=square$ $\bigcirc$ undefined

Explanation:

Step1: Determine the applicable part of the function

Since \(1<4\), we use \(f(x)=\frac{3}{4}x - 3\).

Step2: Substitute \(x = 1\) into the function

Substitute \(x = 1\) into \(y=\frac{3}{4}x - 3\), we get \(y=\frac{3}{4}\times1-3\).

Step3: Simplify the expression

\[

$$\begin{align*} y&=\frac{3}{4}-3\\ &=\frac{3}{4}-\frac{12}{4}\\ &=-\frac{9}{4} \end{align*}$$

\]

Answer:

\(-\frac{9}{4}\)