109-11 Final Exam

Show all work where relevant to earn full credit.

For 1-4, given a line that has a slope of −

3

2

and passes through (-3, 3):

1. State the equation of the line in point-slope form.

2. State the equation of the line in slope-intercept form.

3. State the equation of the line in standard form.

4. Graph the line and label the intercepts:

5. Find the value(s) for 𝑡 for the equation |4𝑡 − 2| = 14

6. Solve the inequality 5(𝑥 − 4) > 2(𝑥 + 8) for 𝑥.

7. Find the exact distance in simplest terms between the points (-4, 7) and (8, -3).

8. Find the compound function 𝑓 ∘ 𝑔(𝑥) for 𝑓(𝑥) = 𝑥

2 + 3 and 𝑔(𝑥) = 2𝑥 − 5.

9. Find the inverse of the function 𝑓(𝑥) =

3𝑥+5

2

.

10. Use the quadratic equation to factor the function 𝑓(𝑥) = 𝑥

2 + 4𝑥 + 8. Show that one of

the two results is correct by evaluating the function at that value.

11. Use the rational zero theorem to find all possible rational zeros of the function

𝑓(𝑥) = 𝑥

3 − 3𝑥

2 − 33𝑥 + 35

then completely factor the function into a set of (𝑥 ± 𝑛) binomials.

You open a high-interest restricted savings account. The account pays 3.00% interest per

year. If you deposit $6000 in the account,

12. find the balance in the account after 10 years if the interest is compounded monthly;

13. find the balance in the account after 10 years if the interest is calculated with

continuous compounding.

The half-life (the time it takes a radioactive element to decay to half of its original quantity)

of the unstable synthetic element fermium is almost exactly 72 hours. A researcher has

manufactured 6 grams of fermium to use in an experiment.

14. Find the exponential constant 𝑘 and write the exponential decay function.

15. The researcher needs at least 2 grams of pure fermium to complete the experiment.

How much time does the researcher have to complete the experiments before the

sample decays to 2 grams?

16. Find the lengths of all sides (approximate to the nearest hundredth when necessary) and

the measures of all angles (in degrees) for the right triangle below:

17. Graph the function 𝑦 = 2 sin (

1

2

𝑥 +

𝜋

3

) + 2.

17

30

18.Solve the triangle with sides 𝑎 = 11 and 𝑏 = 13 and included angle 𝛾 = 56°.

19. Determine the equation of an ellipse centered at (3,2) with a major axis parallel to the

x-axis of length 12 and a minor axis of length 8.

20. Graph the ellipse described above: