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Question about functions

by Siti Atilia
(Kuala Lumpur, Malaysia)










































function


A function diagram is given which f(x)= {(0,1),(1,3),(4,m),(5,11)}.
(a) Find the value of m
(b) State f(x) in terms of x

Comments for Question about functions

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Jan 13, 2013
Function
by: Staff


Answer

Part I

The three known data points {(0,1),(1,3),(5,11)} represent a linear function because you can draw a straight line through all three points.

This is easy to see if you plot the points:



Function – a straight line can be drawn through all three points




(a) Find the value of m for the data point (4,m)

Since you now have a graph of the function, you can read the value of “m” directly from the graph.

(4,m) = (4,9)

m = 9



 Function – Since you now have a graph of the function, you can read the value of “m” directly from the graph.  (4,m) = (4,9)  m = 9




Final Answer – part (a):

m = 9



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Jan 13, 2013
Function
by: Staff


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Part II

(b)State f(x) in terms of x


Since you now know that f(x) is a linear function, you can determine the equation for the function as follows.

A linear function has the following form (slope-intercept format):

f(x) = ax + b

a = slope of equation

b = y-intercept


The slope “a” can be determined first

slope = "rise" over "run", or "rise" DIVIDED BY "run"

slope = (change in "y" values)/(change in "x" values)

slope = Δy / Δx

slope = (y₂ - y₁)/(x₂ - x₁)


The slope can be determined using any two points where the x-y coordinates are known.

I’m arbitrarily choosing the x-y coordinates for the the two points (0,1) and (5,11).


These points are already listed in the proper order (left to right)

They are listed properly as (0,1) and (5,11) because the slope will be calculated as the change of "y" when x increases. In this case "x" will increase from 0 to 5 (left to right).



Calculation of the slope

Points: Left and Right

(0,1) and (5,11)

(x₁, y₁) and (x₂,y₂)

x₁ = 0
x₂ = 5

y₁ = 1
y₂ = 11

slope = (y₂ - y₁)/(x₂ - x₁)

slope = (11 - 1)/(5 - 0)

slope = (10)/(5)

slope = 10/5

slope = 2



“b”, the y-intercept, can be read directly from the graph. It is the point (0,1).

b = 1

The final equation is:

f(x) = ax + b

a = slope of equation = 2

b = y-intercept = 1

f(x) = 2x + 1


Final Answer – part (b):

f(x) = 2x + 1





Thanks for writing.

Staff
www.solving-math-problems.com



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