Back to Prove growth properties of functions — Problem 5 · Task Set 50

Exercises: Prove Growth Properties of Functions

Work through each section in order. For algebraic proofs, show each step clearly. Use variable expressions (not specific numbers) unless the problem asks for a numerical verification.

Grade 9·19 problems·~30 min·Common Core Math - HS Functions·standard·hsf-le-a-1a

Work through problems with immediate feedback

Fluency Practice

For a linear function $f(x) = mx + b$ , the proof shows that $f(x + d) - f(x) = md$ . What does this result confirm about the slope $m$ ?

The slope $m$ equals the constant difference divided by the interval width $d$ .

The slope $m$ equals the constant difference (the result $md$ itself).

The slope $m$ is irrelevant to the constant difference.

The slope $m$ equals the interval width $d$ .