Question

answer each question in detail. (please be specific)
what is the difference between a translation and a reflection?
someone states that the square root of 100 is 50 because 50 + 50 = 100. explain why this is wrong.
is the cubic family a linear function? explain.
what does absolute value mean?
explain both translations from the parent f(x) to the child g(x)

Explanation:

1. Translation vs Rotation: A translation is a transformation that moves every point of a figure or a space by the same distance in a given direction. It's like sliding an object. A rotation is a transformation that turns a figure around a fixed point called the center of rotation. For example, turning a wheel around its axle.
2. Square - root error: The square - root of a number \(x\) is a value \(y\) such that \(y\times y=x\). For \(x = 100\), \(\sqrt{100}=10\) because \(10\times10 = 100\), not \(50\times50=2500

eq100\).

1. Cubic function: A cubic function has the form \(y = ax^{3}+bx^{2}+cx + d\) (\(a

eq0\)). Its graph is a curve (not a straight - line), so it is not a linear function. A linear function has the form \(y=mx + b\) and its graph is a straight line.

1. Absolute value: The absolute value of a real number \(x\), denoted as \(|x|\), is the non - negative value of \(x\) without regard to its sign. So, \(|5| = 5\) and \(|-5|=5\).
2. Function translations: For the functions \(f(x)=x^{3}\) and \(g(x)=(x - 3)^{3}-2\), the \(x-3\) inside the function causes a horizontal translation 3 units to the right (opposite of the sign), and the \(- 2\) outside the function causes a vertical translation 2 units down.

Answer:

1. A translation is a slide and a rotation is a turn.
2. The square - root of 100 is 10 because \(10\times10 = 100\), not \(50\times50\).
3. The cubic family is not a linear function as its graph is a curve, not a straight line.
4. Absolute value is the non - negative value of a number without considering its sign.
5. The function \(g(x)=(x - 3)^{3}-2\) is a translation of \(f(x)=x^{3}\) 3 units to the right and 2 units down.