NAME_______________________________________________

Show your work. NO WORK = NO CREDIT.

 

 

 

General Functions and Relations.

 

1.

 

(6)

For each graph state whether the graph represents a function or a relation. Justify your choice.

 

a.  _function—passes VLT__                                                b.  __relation—fails VLT___________

                                                                               

 

  1. Explain what is meant by “The vertical line test failed.”

 

“The vertical line test failed.” Means the vertical line dropped through the graph of a relation touched two or more points on the graph.

 

 

 

2.

 

(10)

Given the function p(x) = , determine the following:

  1. p(– 5 )

2(– 5) + 5 = – 10 + 5 = – 5    and – 5 – 3 = – 8  or

 

 

 

 

  1. p(6 t + 7)

 

 

 

 

 

 

 

 

3.

 

(10)

Given the function h(x) = , determine the following:

 

Interval notation is not necessary.

  1. Domain   

All x < 3                                                                          Graph of the function h(x)

  1. Range                                                                   

 

All y > 2

 

 

Linear Functions, their Equations and Applications.

 

4.

 

(5)

Determine the slope of the line passing through (4, – 5 ) and  (5, 5).

 

 

5.

 

(5)

Write the equation of the line that passes through (2, 8) and (4, 8). What term would you apply to this line?

 

Y = 8    horizontal line is one possibility

 

 

6.

 

(5)

Write the equation of the line that passes through (6, – 7 ) and  (6, 0). What term would you apply to this line?

 

X = 6  vertical line is one possibility

 

 

 

7.

 

(10)

Write the slope – intercept equation of the line passing through (9, 3) and (4, 8).

 

  So, the line is y = mx + b is what we want. 3 = – 1(9) + b

                                                                                                  12 = b   so the line is y = – x +12

 

 

 

 

8.

 

(8)

Given the line .  Write the equation of the line in STANDARD FORM.

Standard form means no fractions. So multiply every term in the equation by 3, and get

 

3y = – 2x + 15 .   Now get 15 by itself, or, 2x + 3y = 15

 

9.

 

(8)

Write the point – slope equation of a line with slope 7 and passing through (2.2, 3.55).

 

Y – 3.55 = 7(x – 2.2)

 

 

10.

 

(4)

The annual total sales (in thousands) of motorcycles for the years 1998 through 2002 can be modeled by the following: M(t) = 131.4 t + 432.2, where t = 0 corresponds to 1998. What does the model predict for the total annual sales in the years 2004 and 2006?

 

1998  t = 0   so, 2004 t = 6 and 2006 t = 8

 

M(6) = 131.4(6) + 432.2 = 1220.6     and    M(8) = 131.4(8) + 432.2 = 1483.4

 

This means that the model predicts $1,220,600 in 2004 and1 $1,483,400 in 2006 in motorcycle sales, providing trends used for the model remain the same.

 

 

 

 Parallel and Perpendicular Lines.

 

11.

 

(5)

Write the point – slope equation of the line that is parallel to the line y = 2x + 1 and passes through (4, 3).

 

The line parallel to the above has a slope of 2; so the point – slope equation is

 

y – 3 = 2(x – 4)

 

12.

 

(8)

What is the slope of the line that is perpendicular to the line  4x + 9y = 11?

 

First find the slope of the line by transforming the equation into the slope – intercept form.

 

  So, the slope of the perpendicular line is the negative reciprocal of this slope or .

 

 

 

Circles and their Equations.

 

13.

 

8

What is the center and radius of the circle whose equation is ?

 

To find the center and radius we must complete the square two times. The difference here is that we are working on two sides of an equation, and what is added to one side must be added to the other.

 

 

So, the center is (10, – 1) and the radius is 11 (square root of 121).

 

14.

Write the equation of the circle whose center is (4, – 2) with a radius of 6.

 

8

 

 

(x – 4) 2 + (y + 2) 2 = 36 or 6 2 is also acceptable.

 

 

 

 

Bonus 10 points.  Graph the given piecewise function/relation on the grid provided and complete the sentences.

 

 

 

J(x) =                     

 

The graph represents a ___relation____. How do you know? It fails the VLT at x = 0.

 

Each piece of the graph is a ___linear___ function.