The height, in feet, of an object x seconds after it is thrown straight up in the air can be...

1. TRANSLATE the function notation

• Given: \(\mathrm{h(1.4) = 1.64}\)
• In function notation \(\mathrm{h(x)}\):
  • \(\mathrm{x}\) is the input value
  • \(\mathrm{h(x)}\) is the output value
• Here: input = 1.4, output = 1.64

2. INFER what the input and output represent from context

• The problem states: "height, in feet, of an object x seconds after it is thrown"
• This tells us:
  • \(\mathrm{x}\) represents time in seconds
  • \(\mathrm{h(x)}\) represents height in feet

3. TRANSLATE the equation into English

• \(\mathrm{h(1.4) = 1.64}\) means:
  • When \(\mathrm{x = 1.4}\) seconds
  • The height \(\mathrm{h(x) = 1.64}\) feet
• Complete interpretation: "The height of the object 1.4 seconds after being thrown is 1.64 feet"

Answer: A

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse which number represents time and which represents height in function notation.

They might think the first number (1.4) is always the height and the second number (1.64) is always the time, regardless of the function notation structure. This leads them to interpret it as "the height is 1.4 feet when the time is 1.64 seconds."

This may lead them to select Choice B (The height of the object 1.64 seconds after being thrown straight up in the air is 1.4 feet.)

Second Most Common Error:

Poor INFER reasoning about context: Students may not connect that this is describing height versus speed, or they may not understand what the function output represents.

Without recognizing that \(\mathrm{h(x)}\) specifically models height, they might think 1.64 could represent speed or some other physical quantity.

This may lead them to select Choice D or causes confusion and guessing.

The Bottom Line:

Function notation problems require careful attention to which value is the input and which is the output, combined with understanding what each represents in the real-world context.