APPC Unit 5 Review

Definitions

100

In a logarithmic functions, this describes how input values change.

What is multiplicatively?

200

In a exponential functions, this describes how input values change.

What is additive?

300

In a logarithmic functions, this describes how output values change.

What is additive?

400

In a exponential functions, this describes how output values change.

What is multiplicative?

500

This is the pattern seen in an exponential plot that has been plotted on a semi-log plot.

What is linear?

Evaluating Logarithms

100

log₅(25)

2

200

log₄(1/16)

-2

300

ln e³

3

400

log₆₄4

1/3

500

log₄₉(1/7)

-1/2

Inverse and Composite Functions

100

This is the first step to set up an inverse function analytically.

What is switch x and y?

200

When evaluating a composite function, this is where to begin.

What is the innermost function?

300

If f(x) = x³-1 and g(x) = 2x - 3, what's g(f(x))?

2x³ - 5

400

If f(x) = x³-1 and g(x) = 2x - 3, what's f(g(x))?

8x³ - 36x² + 54x - 28

500

Find the inverse of the function:

2x - 9

7x + 2

(yeah, the formatting is trash)

(-2x - 9) / 7x - 2

Solving Exponential Equations

100

What are all values of x for which 3^2x = 9

x = 1

200

Solve:

3(2^{x - 4}) = 24

x = 7

300

The function is k given by k(x) = 6e^{x + 2}. Solve for k(x) = 11

x = ln (11/6) - 2

400

Solve:

3^{x - 1} = 9^{2x + 5}

x = -11/3

500

Solve for x:

9 = -5 + 2e^x/5

x = 5 ln (7)

Solving Logarithmic Equations

100

Solve

2 = log₃(x - 4)

x = 13

200

Solve: 2 ln (x) = 10

x = e⁵

300

Rewrite as a single natural logarithm without negative exponents:

4 ln x - 1/2 ln y

ln ( x⁴ / sqrt(y) )

400

Rewrite as a single logarithm base 10 without negative exponents in any part of the expression:

log (x + 5) - 3 log (x - 2) - log 4

log ( (x + 5) / (4 (x - 2)^3) )

500

If f(x) = log (x) + log (x+4) and g(x) = log (x+18), what are all x-coordinates of the points of intersection of the graphs of f and g?

x = 3

x = -6 is NOT in the domain