Non-Linear Functions and Models

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The graph of a non-linear functions must cross at least one axis.

A ratio of two linear functions is always non-linear.

The graph of a quadratic function f(x) = ax²+bx+c (a

0) is always a parabola.

Some parabolas cross neither axis.

a⁹ = (a³)³

a⁶ = a³a²

a⁵ = a³ + a²

a^-2 =

a²

a^1/2

-a^-1/2

10.

(a+b)^1/2 = a^1/2 + b^1/2

11.

f(x) = 2(3^x) is an exponential function.

12.

g(x) = -2(4^2x) is an exponential function.

13.

r(x) = 10x^2.1 is an exponential function.

14.

h(x) = 4(3^x-1) is an exponential function.

15.

log 6 = log 3 + log 3

16.

log 6 = log 3 + log 2

17.

log 9 = (log 3)²

18.

ln 3(1.05)²⁰ = 20 ln (3.15)

19.

-ln 3 = ln(-3)

20.

An investment earning 20% interest compounded twice a year is better than one earning 19.7% interest compounded continuously.

21.

(1 + 0.03)^-3x can be entered in a graphing calculator as 1.03^(-3*x)

22.

Any situation that can be modeled with a sine curve can also be modeleld with a cosine function.

23.

Any situation that can be modeled with a cosine curve can also be modeleld with a sine function.

24.

sin(x+y) = sin(x) + sin(y)

True/False Quizzes for Applied Calculus Topic: Non-Linear Functions and Models (Chapter 2)