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MATH / Consider the function f(x) = begin{cases} ax^2 & text{if } x geq a, ax +2a& text{if } x <a, end{cases} where a is some number. What is the largest value of a such that the graph o…

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problem

Consider the function \[ f(x) = \begin{cases} ax^2 & \text{if } x \geq a,\\ ax +2a& \text{if } x <a, \end{cases} \]where aa is some number. What is the largest value of aa such that the graph of y=f(x)y=f(x) intersects every horizontal line at least once?
Plain-text mathematical notation (without MathML)
Consider the function \[ f(x) =
\begin{cases}
ax^2 & \text{if } x \geq a,\\
ax +2a& \text{if } x <a,
\end{cases}
\]where a is some number.

What is the largest value of a such that the graph of y=f(x) intersects every horizontal line at least once?
Original LaTeX notation
Consider the function \[ f(x) =
\begin{cases}
ax^2 & \text{if } x \geq a,\\
ax +2a& \text{if } x <a,
\end{cases}
\]where $a$ is some number.

What is the largest value of $a$ such that the graph of $y=f(x)$ intersects every horizontal line at least once?

level

Level 5

type

Algebra

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Source and history

task_id
185479d3-7eab-571c-9417-6def9d6786df
task_key
algebra--test--185479d3-7eab-571c-9417-6def9d6786df
task_revision_id
1
config / split
algebra / test

Official source

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