Pre-Calculus Test 2.6 – 3.4
Non-calculator page
Find the equation, in standard form, of a circle given the following information.
1. Center (-3, 5) and radius 9.
2. Center (-2, 3) and tangent to the line x = 1.
3. Center (5, 8) and the point (10, 13) in on the circle.
4. Diameter of the circle passes through (-3, 5) and (3, 7)
Find the vertex of the following functions and the x-intercept(s) if they exist (you may want to sketch
them).
5. f(x) = (x + 2)2 + 7
Vertex ____________ x-intercept(s) _______________
6. f(x) = 3x2 – 24x + 36
Vertex ____________ x-intercept(s) _______________
7. f(x) = 4x2 +12x + 9
Vertex ____________ x-intercept(s) _______________
Find the Domain and Range. Determine if the relation is a function.
8. R = {(-2, 5), (-2, 3), (4, 8), (2, 1)}
Domain _____________________
Range_______________________
Function?________
Range_______________________
Function?________
Range_______________________
Function?________
9. W = {(-2, 3), (2, 3), (4, 3), (5, 3)}
Domain _____________________
10. R = {(-2, 5), (4, 3), (-4, 8), (-2, 5)}
Domain _____________________
Find the implied domain
11. 𝑓(𝑥) =
7
𝑥+2
√
12. 𝑓(𝑥) = √2𝑥 − 5
Find the vertex and the x-intercept(s) if they exist.
13. f(x) = -16t2 + 64t + 48
Vertex ____________ x-intercept(s) _______________
14. The total revenue for Rapheal’s Soccer Clinic is given as the function R(x) = 100x - .1x2 where x is
the number of students per month. How students should he accept to maximize his revenue?
a. How many students?
b. What would the revenue be?
15. Find a pair of numbers whose product is a maximum if two times the first number plus the
second number is 48.
a. What are the two numbers?
b. What is their product?
16. Lance wants to fence in his cattle, using an existing river as one of the borders. He has 220 ft. of
fencing to use, but wants to give the cattle the maximum room to graze. What dimensions
should he make the fence line?
a. Label the dimensions to make the maximum area.
b. What is the area of the pen?
Solve the following variation problems
17. Suppose that y varies directly as the square root of x, and that y = 36 when x = 16. What is y
when x = 20?
18. Suppose that z varies jointly as the square of x and the cube of y, and that z = 768 when x = 4
and y = 2. What is z when x = 3 and y = 2?
19. The volume of a right circular cylinder varies directly as the radius squared times the height of
the cylinder. If the radius is 7 inches and the height is 4 inches, the volume is approximately
615.44 cubic inches. Find the volume if the radius is 10 inches and the height is 12 inches.
20. A video store manager observes that the number of videos rented seems to vary inversely with
the price of the rental. If the store’s customers rent 1050 videos per month when the price is
$3.49, how many videos per month would he expect to rent if he dropped the price to $2.99?
Extra Credit: Find the center and radius of the circle with an equation of x2 + y2 – 4x + 8y – 16 = 0
Pledge:_______________________________________________________________________