7.5/7.6/8A/8B Review

7.5

100

Find x: 

32^3x = 4^2x

x = 0

200

Find x:

25^x = 625^x-5

x = 10

300

Find x: 5^2x = 130

Round to the nearest thousandth.

x = 1.512

400

Find x:

log(x - 3) + log x = 1

x = 5

500

Sylvie invests $5000 in a savings account that earns 2.08% interest compounded annually.  Determine the number of years, to the nearest tenth of a year, that it will take for her investment to triple.

53.4 years.

7.6

100

Condense:

(5 ln x + 2 ln y) - 4 ln x

ln xy²

200

What are the solutions of ln(x - 3)² = 4?

x = 3 +- e²

300

Expand log( x⁴ * the cube root of z⁴ )

4 log x + (4/3) log z

400

Determine, to the nearest tenth of a year, how long it would take for an investment to double at a 3.9% interest rate compounded continuously.

17.8 years

500

Suppose you plan to invest $4200 at an annual rate of 7.5%.  How long will it take, to the nearest hundredth of a year, for you to have $10,000 if the balance is compounded quarterly?

11.67 years

8A

100

Write a reciprocal function that is stretched by a factor of 2 AND translated 2 units up and 3 units to the right from the parent function.

y = (2/(x - 3)) + 2

200

What are the x and y-intercepts of the function y = 12/x?

No x/y-intercepts.

300

Write the domain of the function in interval notation:

y = (x - 1) / (x² - 6x + 5)

(- infinity, 1) U (1, 5) U (5, infinity)

400

Find the horizontal and vertical asymptotes AND the x and y-intercepts of the function:

y = (x² + x - 12) / (x² - 4)

HA: y = 1

VA: x = 2 and x = -2

x-intercepts: (-4, 0) and (3, 0)

y-intercept: (0, 3)

500

What is/are the point(s) of discontinuity for the function:

y = (x - 5) / (x² + 1)

Removable or non-removable?

x = i and x = -i

Nonremovable

8B

100

Find the horizontal asymptote of y = 2x / x - 3

y = 2

200

What is the difference between a removable and non-removable point of discontinuity?

Removable: hole

Non-removable: asymptote 

300

When is a horizontal asymptote nonexistent? 

When the degree of the numerator is greater than the degree of the denominator.

400

What is the domain of the function: 

y = (x² - 3x - 4) / (x - 4)

What does this value represent?

x ≠ -4

Hole/Removable point of discontinuity

500

GRAPH the function and calculate the y-intercept, the x-intercept, the horizontal asymptote and the vertical asymptotes.

y = (x + 3) / (x² - 6x + 5)

HA: y = 0

VA: x = 1, x = 5

y-intercept: (0, 3/5)

x-intercept: (-3, 0)