M305G – Practice Test #1
NAME:______________________________________
SOCIAL:_____________________________________
No calculators allowed. Show all work. When graphing be sure to label the axes, draw
the graph large, and be neat. Good luck!
#1. (20 points) Consider a circle given by the equation
2x2 + 2y2 + 8x + 7 = 0
A) Find center and radius of this circle.
B) Write an equation of the line that passes through the center of the circle and has slope
equal to the radius of the circle.
C) What are the x- and y-intercepts of this line?
D) Find the distance from the center of the circle to the y-intercept of the line.
#2. (20 points) Consider the function
f(x) = 1 – (x – 2)3
A) Sketch the graph of this function using transformations. Make sure to specify the
function to which you are applying transformations, and label all the transformations.
B) Find the average rate of change between x and 2 (where x is not equal to 2).
C) Sketch the secant line between 2 and 4 on the graph in part A), and find its slope.
#3. (20 points) Suppose you know that f(x) is a polynomial function which has degree 5,
zeros at 0, 3, -2, so that zeros at 3 and –2 have multiplicity 2 each, and f(1) = 36.
A) Write down an equation for this function.
B) What are the x-intercepts of f(x)? At which of them does f(x) touch and at which does
it cross the x-axis?
C) Indicate the interval at which f(x) is above and at which it is below the x-axis.
D) Sketch the graph of f(x), labeling the x-intercepts.
3( x 2  9)
#4. (20 points) Let R( x) 
.
5( x 2  6 x  9)
A) Find the domain of this function.
B) Find the vertical asymptotes of this function, if any.
C) Find the horizontal asymptotes of this function, if any.
D) Find the x- and y-intercepts of this function.
#5. (20 points) Consider the following equations.
y  1 x
y  2 x 3  3x  1
y 2  25  x 2
y2  x  2
y
3x  1
x2  3
| y | x
For each of them do the following.
A) Determine whether an equation represents y as a function of x or not. Why or why
not?
B) For each one that is a function of x, find the domain and the range.
C) Some of the functions can be identified as polynomial or rational functions of x.
Which ones are which? Specify the degree for the polynomial functions.