Hour: _____Name: ______

Date: ______

Pre-Calculus: Chapter 1 Review

  1. Let .

a)Explain why the number 5 is not in the domain of .

b)Explain why the number 25 is not in the domain of .

c)Find the domain of .

  1. Find a function with the indicated domain.

a)

b)

c)

  1. Let .

a)Identify the domain and the range of .

b)Find .

c)For what value(s) of does ?

d)Algebraically find the solution to the inequality .

e)Accurately graph on the axes provided. Label the intercepts.

(THINK!: Does your graph confirm your answers to all of the above problems?)

f)Evaluate the difference quotient , .

  1. The graph of is shown at right.

Sketch the graph of and describe the sequence of transformations that occurs from the parent function to obtain the graph you sketched.

  1. Given the graph of at right, sketch the graph of , describe the sequence of transformations that occurs from to obtain the graph you sketched.
  1. The domain of the one-to-one function is and its range is . Find the domain and range of each of the following functions.

Function / Domain / Range
  1. An isosceles triangle is inscribed in the curve , as shown.

a)Express the area of the triangle as a function of x.

b)Determine the domain of the area function.

c)What is the maximum area of the triangle?

  1. Consider a square.

a)Write the area of a square as a function of the length of its diagonal.

b)Express the length of the diagonal of a square as a function of its area.

c)What is the relationship between the two functions you just wrote? Does your answer need any qualifications or stipulations? Are these justified in the context of the problem?

  1. The function is either always increasing or always decreasing on the interval . If , then how does the value help us decide whether is increasing or decreasing? Be specific.
  1. Algebraically determine whether each function is even, odd, or neither.

a) b)

  1. Consider even functions.

a)What does it mean algebraically for a function to be even?

b)What does it mean graphically for a function to be even?

c)Use your algebraic definition to show that is even and is not.

d)Confirm your findings in part (c) using the graphs of and . Explain how you did this.

  1. The graph of passes through the points , , and .

a)Name three additional points on the graph of if is odd.

b)Name three additional points on the graph of if is even.

c)Name three points that cannot be on the graph of if is one-to-one.

d)Name three points on the graph of if is one-to-one.

  1. Let .

a)Find the function such that .

b)Algebraically verifythat and are inverses of each other.

c)Graphically verify that and are inverses of each other. Explain how you did this.

  1. Refer to the graph of h at right. (As always, express your answers in interval notation, where appropriate.)

a)Find .

b)Find .

c)For what value(s) of x is ?

d)On what interval is ?

e)On what interval is h increasing?

f)State the domain of .

g)State the range of .

h)What is the minimum value of h on the interval shown?

i)What type of function is h (even, odd, or neither)?

j)Explain why h is a function.

  1. Given:

is a linear function

Find:

  1. Answer always, sometimes, or never.

a)The graph of a relation ______passes the vertical line test.

b)The graph of a function ______passes the horizontal line test.

c)A one-to-one function is ______even.

d)If a function has an inverse, then it is ______one-to-one.

e)A one-to-one function is ______either always increasing or always decreasing.

f)The composition of an odd function and its inverse is ______odd.

g)An odd function ______has an inverse.

h)If and are functions, then is ______a function.

i)Quadratic functions are ______even.

j)Quadratic functions are ______one-to-one.

k)Cubic functions are ______odd.

l)Cubic functions are ______one-to-one.

m) is ______equal to .

n)A function is ______its own inverse.

o) is ______called a relative maximum if there exists an interval that contains and if implies .

  1. Let , where and . Find the domain of h.
  1. The equation shows the sum of the measures of the interior angles of a polygon as a function of the number of sides of the polygon (i.e., input is the number of sides, output is the sum of the measures of the interior angles).

a)Find .

b)What are the inputs and outputs of the inverse function?

c)What is the domain of the inverse function?

  1. Let AB = 15.

a)Find the value of a.

b)Write the slope-intercept equation of .

c)Find the coordinates of D.