aroc and justifications proficiency

Question 1

reason for f(x) having an inverse:

Answer 1

f is one to one

for every input value there is only one output and viceversa.

Question 2

reason for f(x) NOT having an inverse:

Answer 2

f is not one to one

there is one input value that produces two outputs OR there are two inputs that produce the same output.

Question 3

the reason a table of values of f can be best modeled by a:

LINEAR

Answer 3

the rate of change (1st difference of the output values) over consecutive equal-length input value intervals is constant.

Question 4

the reason a table of values of f can be best modeled by a:

QUADRATIC

Answer 4

the change in the average rates of change (2nd differences of the output values) over consecutive equal-length input value intervals is constant.

Question 5

the reason a table of values of f can be best modeled by a :

EXPONENTIAL

Answer 5

there is a common ratio between consecutive output values over consecutive equal-length input value intervals.

Question 6

the reason a table of values of f can be best modeled by a:

LOGARITHMIC

Answer 6

there is a common ratio between consecutive input values over consecutive equal-length output value intervals.

Question 7

AROC of f(x) on [a,b]: f(b)-f(a) / b - a

AROC of f(x) will be GREATER at

Answer 7

x = c if c>b and f is concave UP (ROC of f is increasing)

Question 8

AROC of f(x) on [a,b]: f(b)-f(a) / b - a

AROC of f(x) will be SMALLER at

Answer 8

x = c if c>b and f is concave DOWN (ROC of f is decreasing)

Question 9

use the AROC of f(x) on [a,b] to approx. f(c) ~ (f(b)-f(a)/b-a)(x-a)+f(a)

the estimate of f(c) using the AROC is LESS than the estimated value using the model if f is :

Answer 9

if f is concave UP / the ROC of f is increasing

and c>b

Question 10

use the AROC of f(x) on [a,b] to approx. f(c) ~ (f(b)-f(a)/b-a)(x-a)+f(a)

the estimate of f(c) using the AROC is GREATER than the estimated value using the model if f is:

Answer 10

concave UP // ROC of f is increasing

and a < c < b