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Algebra / Linear functions Difficulty: Easy

$f (x) = 8 x + 4$

The function $f$ gives the estimated height, in feet, of a willow tree $x$ years after its height was first measured. Which statement is the best interpretation of $4$ in this context?

The tree will be measured each year for $4$ years.

The tree is estimated to grow to a maximum height of $4$ feet.

The estimated height of the tree increased by $4$ feet each year.

The estimated height of the tree was $4$ feet when it was first measured.

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Explanation

Choice D is correct. It's given that the function $f (x) = 8 x + 4$ gives the estimated height, in feet, of a willow tree $x$ years after its height was first measured. For a function defined by an equation of the form $f (x) = m x + b$ , where $m$ and $b$ are constants, $b$ represents the value of $f (x)$ when $x equals 0$ . It follows that in the given function, $4$ represents the value of $f (x)$ when $x equals 0$ . Therefore, the best interpretation of $4$ in this context is that the estimated height of the tree was $4$ feet when it was first measured.

Choice A is incorrect and may result from conceptual errors.

Choice B is incorrect and may result from conceptual errors.

Choice C is incorrect and may result from conceptual errors.