Quiz Chapter 05.01: Background of Interpolation

1. The number of different polynomials that can go through two fixed data points $x_{1},y_{1}$ and $x_{2},y_{2}$ is

0

1

2

infinite

2. Given $n+1$ data pairs, a unique polynomial of degree _____ passes through the $n+1$ data points.

n+1

n+1

or less

n

n

or less

3. The following function(s) can be used for interpolation

polynomial

exponential

trigonometric

all of the above

4. Polynomials are the most commonly used functions for interpolation because they are easy to

evaluate

differentiate

integrate

evaluate, differentiate, and integrate

5. Given $n+1$ data points $\left( x_{0},y_{0} \right), \, \left( x_{1},y_{1} \right), \, ... \, , \left( x_{n-1}, y_{n-1} \right), \, \left( x_{n}, y_{n} \right)$ , and assume you pass a function $f \left( x \right)$ through all the data points. If now the value of the function $f (x)$ is required to be found outside the range of the given $x$ -data, the procedure is called

extrapolation

interpolation

guessing

regression

6. Given three data points $\left( 1,6 \right), \, \left( 3, 28 \right), \, \left( 10,231 \right)$ , it is found that the function $y = 2x^{2} + 3x + 1$ passes through all the three data points. Your estimate of $y$ at $x = 2$ is

6

15

17

28