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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

What if, for the linear function

$f(x)$ ,

$m =0 ?$

This means that the above reasoning is invalid.
For how the function is defined above, $m$ cannot equal zero.
It makes things easier, since the growth rate of $f(x)$ simply becomes zero (and thus constant) for all intervals.
It does not change anything, since $Delta f$ is not dependent on $m$ .