Simplify the difference quotient ƒ(x+h)-ƒ(x)/h
ƒ(x) = 4x-3

Verified step by step guidance

1. Step 1: Start by substituting the function \( f(x) = 4x - 3 \) into the difference quotient formula \( \frac{f(x+h) - f(x)}{h} \).
2. Step 2: Calculate \( f(x+h) \) by replacing \( x \) with \( x+h \) in the function \( f(x) = 4x - 3 \). This gives \( f(x+h) = 4(x+h) - 3 \).
3. Step 3: Expand \( f(x+h) = 4(x+h) - 3 \) to get \( 4x + 4h - 3 \).
4. Step 4: Substitute \( f(x+h) = 4x + 4h - 3 \) and \( f(x) = 4x - 3 \) into the difference quotient: \( \frac{(4x + 4h - 3) - (4x - 3)}{h} \).
5. Step 5: Simplify the expression in the numerator: \( (4x + 4h - 3) - (4x - 3) = 4h \). The difference quotient becomes \( \frac{4h}{h} \).