Question

The graph represents f(x) = [x]+3.

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What is f(-2.2)?
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Answer 1

Let's see

`\\ \rm\Rrightarrow f(x)=[x]+3`

`\\ \rm\Rrightarrow f(-2.2)`

`\\ \rm\Rrightarrow [-2.2]+3`

`\\ \rm\Rrightarrow -2+3`

`\\ \rm\Rrightarrow 1`

So

• f(-2.2)=1

Answer 2

`\large\text{$ f(-2.2)=1 $}`

Explanation:

Given function:

`\large\text{$ f(x)=\left\lceil x \right\rceil+3 $}`

This is a Ceiling Function, denoted by the square brackets [ ] with the bottom part missing.

When graphing a Ceiling Function:

• open dot means "not including"
• solid dot means "including"

The Ceiling Function gives us the nearest integer up.

So the ceiling of x = -2.2 is -2, as the greatest integer that is more than (or equal to) -2.2 is -2

Therefore:

`\large\begin{aligned}f(-2.2) & =\left\lceil -2.2 \right\rceil+3\\& = -2+3\\& = 1\end{aligned}`

This is confirmed when using the graph to solve.

To find f(-2.2), locate x = -2.2 on the graph.

Trace up vertically until a step is reached.

The step in this part is not including -3 and including -2, so this confirms that x = -2.2 is in this interval.

Trace along horizontally to the y-axis to find the corresponding y-value, which is 1.

Therefore, f(-2.2) = 1