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Chapter 1: Problem 9

Look at the accompanying table. a. Find \(p(-4), p(5),\) and \(p(1)\) b. For what value(s) of \(n\) does \(p(n)=2 ?\) $$ \begin{array}{l|cccccccccc} \hline n & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline p(n) & 0.063 & 0.125 & 0.25 & 0.5 & 1 & 2 & 4 & 8 & 16 & 32 \\ \hline \end{array} $$

Short Answer

Expert verified
p(-4) = 0.063, p(5) = 32, p(1) = 2. p(n) = 2 when n = 1.

Step by step solution

01

Locate Values in the Table

To find the values for part (a), locate the given n-values (-4, 5, 1) in the table and identify their corresponding p(n) values.
02

Identify p(-4)

In the table, look at the row where n = -4. The corresponding p(n) value is 0.063. So, p(-4) = 0.063.
03

Identify p(5)

In the table, look at the row where n = 5. The corresponding p(n) value is 32. So, p(5) = 32.
04

Identify p(1)

In the table, look at the row where n = 1. The corresponding p(n) value is 2. So, p(1) = 2.
05

Determine When p(n)=2

To answer part (b), locate the value of 2 in the p(n) row of the table. Identify the corresponding n-value. Here, p(n) = 2 when n = 1.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

function tables
Function tables are a great tool for visualizing the relationship between inputs and outputs in a function.
Each row typically contains input values (often denoted as n) and their corresponding output values (often denoted as p(n)).
In our exercise, we have a table where the first row lists different n values ranging from -4 to 5, and the second row shows their p(n) values.
Using function tables makes it easy to find the value of a function for a given input and to see how the function behaves across different values.
So, to use the table, just match the input you are interested in with its corresponding output.
locating values
Locating values in a function table is straightforward.
Simply find the given input value (n) in the first row, and then look directly below it to the second row to find the corresponding function value (p(n)).
For instance, to find p(1) in our table:
  • Locate 1 in the row of n values.
  • Look at the value directly below it in the p(n) row, which is 2.
Thus, p(1)=2.
This method is the same for any input value you are looking for, whether it's positive, negative, or zero.
function notation
Function notation is a way to represent functions mathematically.
For example, p(n) means that p is a function of n. This tells us that n is the input to the function, and p(n) is the output.
In our exercise, the function notation p(-4) indicates that -4 is plugged into the function p.
  • We find p(-4) by looking at the input value -4 in the table.
  • The corresponding p(n) value is 0.063.
So, p(-4)=0.063.
inverse function value
An inverse function swaps the roles of the input and output in a function.
Instead of finding the output for a given input, you find the input that gives a specified output.
For example, in part (b) of our exercise, we need to find the value of n when p(n)=2.
  • Look through the p(n) row to find the value 2.
  • See which value of n is directly above it.
In this case, p(n)=2 when n=1.
This is useful when you know the output and need to determine the corresponding input.

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Most popular questions from this chapter

Given \(T(x)=x^{2}-3 x+2,\) evaluate \(T(0), T(-1), T(1),\) and \(T(-5)\).

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