Question

question 39 points 2

find the number of units the function \\(y = |x + 3|\\) is translated from the parent function.

shifted 3 units upwards from the origin

shifted 3 units left from the origin

Explanation:

Identify the parent function

The given function is \(y = |x + 3|\). The parent function of an absolute value function is:

$$ y = |x| $$

Analyze the horizontal translation

A horizontal translation of a function \(f(x)\) is represented by \(f(x - h)\), where:

• If \(h > 0\), the graph shifts right by \(h\) units.
• If \(h < 0\), the graph shifts left by \(|h|\) units.

For \(y = |x + 3|\), we can rewrite the expression as:

$$ y = |x - (-3)| $$

Since \(h = -3\), the graph is translated \(3\) units to the left.

Determine the shift relative to the origin

The vertex of the parent function \(y = |x|\) is at the origin \((0, 0)\).
Translating the function \(3\) units to the left moves the vertex to \((-3, 0)\).
Therefore, the function is shifted \(3\) units left from the origin.

Answer:

• Shifted 3 units upwards from the origin
• Shifted 3 units left from the origin (Correct answer)