Name:______
MAT 126 – Precalculus October 10, 2012
Professor PestieauExam 1 – Algebraic Functions
Multiple-Choice Questions
Circle the correct answer for the following questions. [5 pts each]
For questions 1 – 2 below, consider the points , and in the -plane. Let be the line passing through points and .
1.What is the equation of the line perpendicular to that passes through ?
a.b.
c.d.
2.What is the equation of the circle centered at passing through ?
a.b.
c.d.
3.What can you say about the graph of ?
a.It is symmetric about the y-axis.
b.It is symmetric about the x-axis.
c.It is symmetric with respect to the origin.
d.It has no symmetries.
4. What is the domain of the function?
a.b.
c.d.
5.If , is a zero of and is a vertical asymptote of the graph of , then what are the values of and ?
a.b.
c.d.
6.What is the range of the quadratic function , where is some real coefficient?
a.b.
c.d.
7.The graph of is also…
a.…the graph of shifted horizontally 3 units to the left.
b.…the graph of shifted horizontally 4 units to the left.
c.…the graph of shifted vertically 3 units upwards.
d.…the graph of shifted vertically 4 units upwards.
8.If a parabola passes through the origin and its line of symmetry is the vertical line , then which of the following equations could not describe such a parabola?
a.b.
c.d.
9.A polynomial function has a zero at of multiplicity 2 , another zero at of multiplicity 3, and a third zero at of multiplicity 5. If the graph of intersects the y-axis at 216, what is ?
- b.
c.d.
10.Consider the rational function given by
.
The graph of has…
- …two vertical asymptotes, one horizontal asymptote, and no x-intercept.
- …two vertical asymptotes, one horizontal asymptote, and one x-intercept.
- …three vertical asymptotes, one horizontal asymptote, and one x-intercept.
- …three vertical asymptotes, one horizontal asymptote, and no x-intercept.
- …three vertical asymptotes, no horizontal asymptote, and no x-intercept.
Bonus Question[5 pts]
Find the domain of , write in lowest terms, and find all the asymptotes of the graph of .
Show all your work on the following problems to receive full credit.
Problem 1[10 pts]
Consider the curve described by the equation
.
a)Using the graphs provided below, plot this curve using 3transformations. Label 2 points on the initial curve and follow these points through all stages of the transformation.
b)What is the range of the function ?
Problem 2[10 pts]
A parabolic arch has a span of 120 feet and a maximum height of 25 feet.
a)Graph the arch below using a suitable x and y rectangular coordinate system. Findthe equation of thisparabolic arch. Show your scale and any relevant points on the arch.
b)How far would a 6-feet-tall man have to walk away from the midpoint of the arch legs before hitting the arch with his head?
Problem 3[5 pts]
Explain why the graph of is necessarily symmetrical with respect to the y-axis whenever is an odd function.
Problem 4[10 pts]
Let be the polynomial function given by
.
a)List all potential zeros of .
b)Find the only zero of and factor completely. Show your algebraic work.
Problem 5[15 pts]
Consider the rational function given by
.
a)Find , the domain of , and write in lowest terms.
Note: the formula for the difference of two cubes is.
b)Locate and identify all the asymptotes of , the graph of . Show your algebraic work.
c)Find the point whereintersects its non-vertical asymptote. Show your algebraic work.
Bonus Problem 1[5 pts]
Find the equation of the line passing through the centers of the two circles described below.
Bonus Problem 2[5 pts]
If , and are three points on the -plane, find the slope of the bisector of angle . Round your answer to the nearest tenth.