? Exercise 2.5 .2 Given the description of the transformed absolute value function write the equation. The absolute value function is horizontally shifted left 2 units, is vertically flipped, and vertically shifted up 3 units. $$ f(x)=\square $$

Question

UpStudy AI · Accepted Answer

To write the equation of the transformed absolute value function based on the given transformations, we'll follow these steps:

1. **Horizontal Shift Left 2 Units:**
   - This affects the $$ x $$-component inside the absolute value.
   - Shifting left by 2 units means replacing $$ x $$ with $$ x + 2 $$.
   - So, the expression becomes $$ |x + 2| $$.

2. **Vertical Flip:**
   - Flipping the graph vertically changes the sign of the absolute value function.
   - This introduces a coefficient of $$-1$$ in front of the absolute value.
   - Now, the expression is $$ -|x + 2| $$.

3. **Vertical Shift Up 3 Units:**
   - Shifting up by 3 units affects the constant term outside the absolute value.
   - Adding 3 to the expression gives $$ -|x + 2| + 3 $$.

**Final Equation:**
$$
f(x) = -|x + 2| + 3
$$
$$ f(x) = -|x + 2| + 3 $$

? Exercise 2.5 .2 Given the description of the transformed absolute value function write the equation. The absolute value function is horizontally shifted left 2 units, is vertically flipped, and vertically shifted up 3 units. \( f(x)=\square \)

Solución de tutoría real

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Algebra Questions