Summer Mathematics Requirement for students scheduled for

Precalculus

Over the summer you are responsible for reviewing prerequisite topics in Algebra, in preparation for your Precalculus class next year.

This is a summer packet for students entering into Precalculus course. This packet is due on the first day of school and will be graded upon completion as a homework grade. Preliminary assessment will be based on the topics covered in this packet, and graded as a quiz administered during the first week of school.

To assist you in completing this assignment there are many online resources. Some highly recommended resources are www.mathtv.com , http://www.coolmath.com/algebra http://mathforum.org/dr.math/ and https://www.khanacademy.org/math/algebra2, http://algebra1cc.flippedmath.com/31-standard-form-equations-of-lines.html http://algebra1cc.flippedmath.com/unit-8-functions.html

Sincerely,

The Mathematics Teachers at Teaneck High School

Name__________________________
Precalculus – Summer Assignment –	Score:

Show each step of your work.

1. Find the slope of the line that passes through each pair of points.

a.	(2, 7) , (5, 2)

c.	Find the slope of AB

b. (-2 , -3) , (4 , 6)

d. Find the slope of CD

2. Graph each equation.

4
a.	y  3 x2	b. 6x+3y = 9	c. x=3	d. y=-4

y 
3. Write the equation of the line in slope-intercept form.

a.	m = -3 and passed through the point (-2, 3)	b. line passes through the point (5, -3) and (-1,-15)

4. Write the slope-intercept form for an equation of the line that passes through the given point and is i.	parallel to the graph of the given equation
ii. perpendicular to the graph of the given equation

a.	(-2, 3), y = 5x – 2	b. (1, 4), y = -3x + 2

5. State the domain and range of each function.

a.

b.

c.

d.

y  x3  5x  2

y= (x+2)2 – 4.

𝑦 = √2𝑥 + 10

2x 3

x2  x  2

6.

7. Find and simplify the difference quotient for f(x) = x2 + 9x – 8.

8. Identify the open interval(s) where the function is increasing, decreasing, and constant.

9. Determine which function is one-to-one. Explain your reasoning.

a. y =| 𝑥 − 3|	b. y = x3 - 1	c. y = x2 + 4	d. y = x3 -3x +1

2
𝑥 + 1,𝑥 ≥ −4
10. Given the piecewise function: f(x) = {2𝑥 − 1,𝑥 < −4, what is the value of f(0) and f(-4)?

11. Given: f(x) = √𝑥, write an equation that has been shifted up 3 units, left 7, and reflected over the x-axis.

12. Use a graphing calculator to find all local maxima and minima of the function f(x) = x3 – 3x2 – 9x + 9.

13. Find the inverse of the given function f (x) = {(5, 0), (0, 5), (7, – 8) (3, 2)}.

14. Given f(x) = x2 and g(x) = 6 - 4x, find f(g(x)).

15. Use the graphing utility to determine if f(x) =3x3 – 2x is even, odd, or neither. Confirm your answer algebraically.

16. Given h(x) = - (x+4)3 +4.

a. State the parent function.

b. State all transformations.

17. Find the inverse of each function.

a.	y  4 x

b.	f x x 52 1

18. Given f x x2 16 and	gx x3 5, find:

a. (f + g)(-4) =?

	
	
g
b.  f 5 ? 	

c. (f – g)(1) = ?

e. (f∙g)(-2) = ?

19. Given f(x) = x+5, h(x) = √𝑥 , and g(x) = x2 – 16, find:

a. g(f(x))

b. 𝑓(𝑔(𝑥))

c. h(g(x))

d. Tell if f(x) and g(x) are the inverses of each other. Explain why or why not.

e. Determine the domain for the composite functions in part (a), (b), and (c).

20. Graph f(x) = x3 -2x2 - 3x, to determine:

a. Local minima of f(x).

b. Local maxima of f(x).

c. Intervals where f(x) is increasing.

d. Intervals where f(x) is decreasing.

e. Is the f(x) even, odd or neither? Verify algebraically.