Question

and domain, find the range values.

1. $y = x^2 - 2x$; domain $= \\{-3, 0, 5\\}$

Explanation:

Step1: Substitute \( x = -3 \) into the function

To find the corresponding \( y \)-value when \( x = -3 \), we substitute \( x = -3 \) into \( y = x^2 - 2x \).
\[

$$\begin{align*} y&=(-3)^2 - 2\times(-3)\\ &=9 + 6\\ &=15 \end{align*}$$

\]

Step2: Substitute \( x = 0 \) into the function

Substitute \( x = 0 \) into \( y = x^2 - 2x \).
\[

$$\begin{align*} y&=0^2 - 2\times0\\ &=0 - 0\\ &=0 \end{align*}$$

\]

Step3: Substitute \( x = 5 \) into the function

Substitute \( x = 5 \) into \( y = x^2 - 2x \).
\[

$$\begin{align*} y&=5^2 - 2\times5\\ &=25 - 10\\ &=15 \end{align*}$$

\]

Answer:

The range values are \(\{0, 15\}\)