Questions: For the equation shown below, solve for y as a function of x and express the result using function notation 32 * x + 4 * y = 16 f(x)= Given f(x)=2 x-2 a) Evaluate f(4)

Solution Steps

For the equation \(32 \cdot x + 4 \cdot y = 16\), solve for \(y\) as a function of \(x\) and express the result using function notation \(f(x)\).

1. Isolate \(y\) on one side of the equation.
2. Express \(y\) in terms of \(x\).
3. Write the resulting expression in function notation \(f(x)\).

Given the equation: \[ 32 \cdot x + 4 \cdot y = 16 \]

First, isolate \( y \) on one side of the equation. Subtract \( 32x \) from both sides: \[ 4y = 16 - 32x \]

Next, divide both sides by 4 to solve for \( y \): \[ y = \frac{16 - 32x}{4} \]

Simplify the fraction: \[ y = 4 - 8x \]

Using function notation, we write: \[ f(x) = 4 - 8x \]

Final Answer