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Nick C
Nick C
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What is the clearest way to indicate various operations along the following lines:

$f(x) = 3x$: The function $f$ multiplies its input by 3.

$g(x) = x-5$: The function $g$ decreases its input by 5.

$h(x) = 2^x$: The function $h$...Raises 2 to the power of its input? Exponentiates its input on a base of 2? Takes 2 to its input?

In the first two cases, I made a choice of whether to refer to the operation's name ("multiply") or a (hopefully) plain language action being performed ("decrease"). For the function $f$, I could have said that it triples its input or increases its input by 200%, but these don't seem to generalize well for the purposes of communicating, and the latter is almost never obvious to students. Similarly, I could have said that the function $g$ subtracts 5 from its input, but I am not convinced this is any simpler than "is decreased"decreases its input by".

Is there a simplest verb phrase for exponents? What do you think is clearest for students if I want to maintain the form "The function $h$ ____________"?

What is the clearest way to indicate various operations along the following lines:

$f(x) = 3x$: The function $f$ multiplies its input by 3.

$g(x) = x-5$: The function $g$ decreases its input by 5.

$h(x) = 2^x$: The function $h$...Raises 2 to the power of its input? Exponentiates its input on a base of 2? Takes 2 to its input?

In the first two cases, I made a choice of whether to refer to the operation's name ("multiply") or a (hopefully) plain language action being performed ("decrease"). For the function $f$, I could have said that it triples its input or increases its input by 200%, but these don't seem to generalize well for the purposes of communicating, and the latter is almost never obvious to students. Similarly, I could have said that the function $g$ subtracts 5 from its input, but I am not convinced this is any simpler than "is decreased by".

Is there a simplest verb phrase for exponents? What do you think is clearest for students if I want to maintain the form "The function $h$ ____________"?

What is the clearest way to indicate various operations along the following lines:

$f(x) = 3x$: The function $f$ multiplies its input by 3.

$g(x) = x-5$: The function $g$ decreases its input by 5.

$h(x) = 2^x$: The function $h$...Raises 2 to the power of its input? Exponentiates its input on a base of 2? Takes 2 to its input?

In the first two cases, I made a choice of whether to refer to the operation's name ("multiply") or a (hopefully) plain language action being performed ("decrease"). For the function $f$, I could have said that it triples its input or increases its input by 200%, but these don't seem to generalize well for the purposes of communicating, and the latter is almost never obvious to students. Similarly, I could have said that the function $g$ subtracts 5 from its input, but I am not convinced this is any simpler than "decreases its input by".

Is there a simplest verb phrase for exponents? What do you think is clearest for students if I want to maintain the form "The function $h$ ____________"?

Source Link
Nick C
Nick C
  • 9.7k
  • 25
  • 60

Clearest verb phrases for operations

What is the clearest way to indicate various operations along the following lines:

$f(x) = 3x$: The function $f$ multiplies its input by 3.

$g(x) = x-5$: The function $g$ decreases its input by 5.

$h(x) = 2^x$: The function $h$...Raises 2 to the power of its input? Exponentiates its input on a base of 2? Takes 2 to its input?

In the first two cases, I made a choice of whether to refer to the operation's name ("multiply") or a (hopefully) plain language action being performed ("decrease"). For the function $f$, I could have said that it triples its input or increases its input by 200%, but these don't seem to generalize well for the purposes of communicating, and the latter is almost never obvious to students. Similarly, I could have said that the function $g$ subtracts 5 from its input, but I am not convinced this is any simpler than "is decreased by".

Is there a simplest verb phrase for exponents? What do you think is clearest for students if I want to maintain the form "The function $h$ ____________"?