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Type: Multiple-Choice
Category: Functions and Relations
Level: Grade 10
Standards: HSF-LE.A.1, HSF-LE.A.1a
Author: nsharp1
Last Modified: 4 years ago

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Functions and Relations Question

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Let

$f(x) = mx+b$ be a real-valued linear function. The following questions will investigate the growth of this linear function, or the value

$Delta f = f(x + Delta x) - f(x)$ , over equal intervals of length

$Delta x$ , where

$Delta x > 0$ .

Grade 10 Functions and Relations CCSS: HSF-LE.A.1, HSF-LE.A.1a

Given the answer in the previous question, which of the following gives the best reasoning as to why one can conclude that a linear function grows by equal differences over equal intervals?

Because the resulting equation for $Delta f$ is also linear, it will increase at a constant rate.
Because there is no slope in the resulting equation, the value of $Delta f$ is constant.
Since the resulting equation for $Delta f$ has no $b$ value, it is independent of the y-intercept. As such, $Delta f$ will increase by equal amounts over equal intervals.
Since $Delta f$ is dependent only on the length of the interval, as long as the interval $Delta x$ is constant, $Delta f$ will be the same.