<< Chapter < Page Chapter >> Page >

Evaluating a function given in tabular form

As we saw above, we can represent functions in tables. Conversely, we can use information in tables to write functions, and we can evaluate functions using the tables. For example, how well do our pets recall the fond memories we share with them? There is an urban legend that a goldfish has a memory of 3 seconds, but this is just a myth. Goldfish can remember up to 3 months, while the beta fish has a memory of up to 5 months. And while a puppy’s memory span is no longer than 30 seconds, the adult dog can remember for 5 minutes. This is meager compared to a cat, whose memory span lasts for 16 hours.

The function that relates the type of pet to the duration of its memory span is more easily visualized with the use of a table. See [link] . http://www.kgbanswers.com/how-long-is-a-dogs-memory-span/4221590. Accessed 3/24/2014.

Pet Memory span in hours
Puppy 0.008
Adult dog 0.083
Cat 16
Goldfish 2160
Beta fish 3600

At times, evaluating a function in table form may be more useful than using equations. Here let us call the function P . The domain    of the function is the type of pet and the range is a real number representing the number of hours the pet’s memory span lasts. We can evaluate the function P at the input value of “goldfish.” We would write P ( goldfish ) = 2160. Notice that, to evaluate the function in table form, we identify the input value and the corresponding output value from the pertinent row of the table. The tabular form for function P seems ideally suited to this function, more so than writing it in paragraph or function form.

Given a function represented by a table, identify specific output and input values.

  1. Find the given input in the row (or column) of input values.
  2. Identify the corresponding output value paired with that input value.
  3. Find the given output values in the row (or column) of output values, noting every time that output value appears.
  4. Identify the input value(s) corresponding to the given output value.

Evaluating and solving a tabular function

Using [link] ,

  1. Evaluate g ( 3 ) .
  2. Solve g ( n ) = 6.
n 1 2 3 4 5
g ( n ) 8 6 7 6 8
  1. Evaluating g ( 3 ) means determining the output value of the function g for the input value of n = 3. The table output value corresponding to n = 3 is 7, so g ( 3 ) = 7.
  2. Solving g ( n ) = 6 means identifying the input values, n , that produce an output value of 6. [link] shows two solutions: 2 and 4.
n 1 2 3 4 5
g ( n ) 8 6 7 6 8

When we input 2 into the function g , our output is 6. When we input 4 into the function g , our output is also 6.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Using [link] , evaluate g ( 1 ) .

g ( 1 ) = 8

Got questions? Get instant answers now!

Finding function values from a graph

Evaluating a function using a graph also requires finding the corresponding output value for a given input value, only in this case, we find the output value by looking at the graph. Solving a function equation using a graph requires finding all instances of the given output value on the graph and observing the corresponding input value(s).

Reading function values from a graph

Given the graph in [link] ,

  1. Evaluate f ( 2 ) .
  2. Solve f ( x ) = 4.
Graph of a positive parabola centered at (1, 0).
  1. To evaluate f ( 2 ) , locate the point on the curve where x = 2 , then read the y -coordinate of that point. The point has coordinates ( 2 , 1 ) , so f ( 2 ) = 1. See [link] .
    Graph of a positive parabola centered at (1, 0) with the labeled point (2, 1) where f(2) =1.
  2. To solve f ( x ) = 4, we find the output value 4 on the vertical axis. Moving horizontally along the line y = 4 , we locate two points of the curve with output value 4: ( −1 , 4 ) and ( 3 , 4 ) . These points represent the two solutions to f ( x ) = 4: −1 or 3. This means f ( −1 ) = 4 and f ( 3 ) = 4 , or when the input is −1 or 3, the output is 4 . See [link] .
    Graph of an upward-facing parabola with a vertex at (0,1) and labeled points at (-1, 4) and (3,4). A line at y = 4 intersects the parabola at the labeled points.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Questions & Answers

write down the polynomial function with root 1/3,2,-3 with solution
Gift Reply
if A and B are subspaces of V prove that (A+B)/B=A/(A-B)
Pream Reply
write down the value of each of the following in surd form a)cos(-65°) b)sin(-180°)c)tan(225°)d)tan(135°)
Oroke Reply
Prove that (sinA/1-cosA - 1-cosA/sinA) (cosA/1-sinA - 1-sinA/cosA) = 4
kiruba Reply
what is the answer to dividing negative index
Morosi Reply
In a triangle ABC prove that. (b+c)cosA+(c+a)cosB+(a+b)cisC=a+b+c.
Shivam Reply
give me the waec 2019 questions
Aaron Reply
the polar co-ordinate of the point (-1, -1)
Sumit Reply
prove the identites sin x ( 1+ tan x )+ cos x ( 1+ cot x )= sec x + cosec x
Rockstar Reply
tanh`(x-iy) =A+iB, find A and B
Pankaj Reply
what is the addition of 101011 with 101010
Branded Reply
If those numbers are binary, it's 1010101. If they are base 10, it's 202021.
extra power 4 minus 5 x cube + 7 x square minus 5 x + 1 equal to zero
archana Reply
the gradient function of a curve is 2x+4 and the curve passes through point (1,4) find the equation of the curve
Kc Reply
Ramesh Reply
test for convergence the series 1+x/2+2!/9x3
success Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?