# Exponential Functions Question

• Apr 4th 2013, 11:13 AM
HelenMc9
Exponential Functions Question
Hi there, I'm trying to do this question but I'm stuck:

Graph the function:
f(x) = (2/3)x, -4
≤x≤1, x∈R

f(-2) lies in the range [1, a]. If a
∈ N, then what is the minimum value of a?

I've drawn the graph, but I don't understand the second part of the question. Could someone please help me?
(Nod)

• Apr 4th 2013, 12:18 PM
Plato
Re: Exponential Functions Question
Quote:

Originally Posted by HelenMc9
Graph the function:
f(x) = (2/3)x, -4≤x≤1, x∈R
f(-2) lies in the range [1, a]. If a ∈ N, then what is the minimum value of a?
I've drawn the graph, but I don't understand the second part of the question. Could someone please help me?

$a = \left\lceil {f( - 2)} \right\rceil$, that is ceiling function.
• Apr 4th 2013, 12:19 PM
emakarov
Re: Exponential Functions Question
You are asked to find the smallest natural number a such that f(-2) ≤ a.
• Apr 4th 2013, 12:27 PM
HelenMc9
Re: Exponential Functions Question
Sorry I don't get it, I'm still really confused ...
• Apr 4th 2013, 12:32 PM
Plato
Re: Exponential Functions Question
Quote:

Originally Posted by HelenMc9
Sorry I don't get it, I'm still really confused ...

What does $f(-2)=~?$
• Apr 4th 2013, 01:02 PM
HelenMc9
Re: Exponential Functions Question
2.25?
• Apr 4th 2013, 01:06 PM
Plato
Re: Exponential Functions Question
Quote:

Originally Posted by HelenMc9
2.25?

OK what is the smallest $a\in\mathbb{N}$ so that $f(-2)\in[1,a]~?$
• Apr 4th 2013, 01:21 PM
HelenMc9
Re: Exponential Functions Question
Eh ... I don't know. What does ' f(-2) ∈ [1,a] ' mean? :/
• Apr 4th 2013, 01:33 PM
Plato
Re: Exponential Functions Question
Quote:

Originally Posted by HelenMc9
Eh ... I don't know. What does ' f(-2) ∈ [1,a] ' mean? :/

You cannot do these questions if you don't know the basics

It means $1\le f(-2)\le a$.