Show:
5.1+5.2: Simplify Exponents + Radicals
6.1-6.5 Exp Growth vs. Decay /
Eval, expand, condense Logs
5.3,5.4+6.6 Solving, + Graph Circles
5.5-5.6: Function operations / Inverse Fxns
100

Rewrite the following expression as an exponent. Then, evaluate.

-(sqrt36)^3

Rewrite:  -(36)3/2

Evaluate: -216

100
Are the following examples of exponential growth or decay? Why?

f(x) = -0.1(4.2)x

g(x) = 2e0.1x

Decay

f(x) = -0.1(4.2)x   Because 4.2 is greater than $1.00 (by ___?)

g(x) = 2e0.1x          Because exponent is positive

100

Solve the equation. (HINT: Where is the x?)

((x-1)/4)^(2/4)=3

x = 37

100

Let f(x) = 3x - 2 and g(x) = x - 4.

Find...

a. (f + g)(x)

b. (f - g)(x)


a. (f + g)(x) = 4x - 6

b. (f - g)(x) = 2x + 2

200

Simplify using properties of Exponents and Radicals

(5^(1/4)/5^(3/4))^3

5-3/2

or

1/5^(3/2)

200

Simplify.

(-4e^(0.5x))^2

16e^x

200

Graph (x+3)2 + (y - 1)2 = 4


Center: (-3, 1)

Radius = 2

200

Let f(x) = 3x - 2 and g(x) = x - 4.

Find (f*g)(x)

(f*g)(x) = 3x2 - 14x + 8

300

Simplify using properties of Exponents and Radicals

3sqrt50-sqrt2

14sqrt2

300

Evaluate the logarithm. Round your answer to the nearest hundredth place.

2 ln(6)

3.58

300

Solve the equation.


log((3x+9)/2)=log(5x+1)

x = 1

300

Let f(x) = 9x2/7 and g(x) = 3x1/7.

a. Find (f/g)(x)

b. Evaluate (f/g)(128)

a. 3x1/7

b. 6

400

Simplify using properties of Exponents and Radicals

root3(27x^8)

3x^2root3(x^2)

400

Rewrite the exponent as a logarithm, or vice versa (Don't need to solve for x)

log7(x+4) = 2

72 = x + 4

400

Solve the equation (HINT: Where is the x?)

e2x + 3 = 18

Round to the nearest hundredth.

x = -0.05

400

Let f(x) = 2x - 1.

Does f(x) have an inverse? If so, find it.


f^-1(x)=(x+1)/2

500

What would you multiply by to get rid of the root in the denominator?

a. 

sqrt3/(2sqrt8)

b.

2/(4-sqrt3)

a.

sqrt8/sqrt8

b.

(4+sqrt3)/(4+sqrt3)

500

Expand or condense the logarithmic expression using the properties of Logarithms.

ln(x) - 3ln(2)

ln(x/8)

500

Solve (Hint: Condense logs if needed) 

ln(x-1) - ln(3) = 3

Round to the nearest hundredth.

x = 61.26
500

Let f(x) = (x - 1)3.

Does f(x) have an inverse? If so, find its inverse, f-1(x).

f-1(x) = 

root3x+1