University of Colorado Denver
Math 1110 Exam 1 Practice Questions
Lana
A. Graphs, Solving Equations and Inequalities.
Solve equations graphically.
1) Use a graphing utility to approximate the real solutions, if any, of the given equation rounded
4
to two decimal places. All solutions lie between -10 and 10. 2x  9  2x  3
Solve quadratic equations by factoring, square root method, completing the square, quadratic formula.
2) Solve the equation by factoring x  2x  35  0 . 
What is the solution set?
2
3) Solve the equation by the square root method x  5  64 . What is the solution set?
2

4) Solve the equation by completing the square x  2x  80 . What is the solution set?
2
5) Find the real solutions, if any, usingthe quadratic formula 3x 11x 10  0 . What is the solution set?
2

Solve radical equations and absolute value equations
algebraically.
6) Find the real solutions of the equation
8x  7 
 7 . What is the solution set?
7) Find the real solutions of the equation 4  3x  2  x . What is the solution set?

8) Find the real solutions of the equation
3x 1  x 1  2 . What is the solution set?
 inequalities algebraically and graphically.
Solve linear inequalities and absolute value

9) Solve the inequality. Express your answer using interval notation.
1
x  4   3x  3
2
10) Solve the inequality. Express your answer using interval notation. 10  4  2 x  7

11) Solve the inequality. Express your answer using interval notation. 3 
2x  6
0
5
12) Solve the inequality. Express your answer using interval notation. 2 x  1  15
13) Solve the inequality. Express your answer using interval notation. x  3  2  5
B. Graphs
Find intercepts of linear and quadratic functions algebraically and graphically.
14) Find the intercepts of the equation. Then sketch a graph of the equation. y  x 2  9
Test an equation for symmetry with respect to the x-axis, y-axis and origin.
15) List the intercepts and test for symmetry. y 2  x  16
Calculate and interpret slope of a line and write the equation of a line in slope-intercept form.
16) Plot the pair of points and determine the slope of the line containing them. Graph the line.
 4,1 ,  0, 5
17) Plot the pair of points and determine the slope of the line containing them. Graph the line.
 2, 4  ,  2,1
Find the equation of a line given a point and the slope of the line, or given two points on the line.
18) Find an equation for the line with slope m  
5
containing the point (7,0). Write in general form.
6
19) Find an equation for the line containing the points P  (5, 2) and Q  (3, 1). Write in slope-intercept
form.
Find the equation of vertical lines and horizontal lines.
20) Find the equation of the vertical line that contains the point  8, 9  .
21) Find the equation of the horizontal line that contains the point  3, 1 .
Find the equation of perpendicular lines and parallel lines. Write answer in slope-intercept form.
22) Find an equation of the line that is perpendicular to y 
5
x and passes through the point  4,5  .
4
23) Find the equation of a line that is parallel to the line y  15x containing the point 3,4 .
Write the standard form of the equation of a circle and graph the circle.
24) Find the standard form of the equation of 
the circle having the following properties.
Center at the origin.

Containing the point 6,6.
25) Write the standard form of the equation of the circle with radius r = 5 and center h,k   3,4.

26) Write the standard form of the equation of the circle x 2  y 2  3x  4 y  4  0 . Find the center and radius.
3. Functions and Their Graphs

Determine whether a relation represents a function
27) Determine if the following relation represents a function. If it is a function, state the domain and range.

a)
3,1,4.2,5,3,6,1.
b)
1,1,2,2,2,4,3,9
Evaluate functions.
28) For the function f defined by f ( x)  2 x 2  5x  8 find the following values. Simplify your answer.
a) f (2)
b) f ( x)
c)  f ( x)
d) f ( x  h)
Evaluate the difference quotient where f is linear as well as quadratic.
29) Find the difference quotient of f, that is, find
f ( x  h)  f ( x )
, h  0, for the following functions.
h
a) f ( x)  5 x  2 Simplify your answer.
b) f ( x)  5 x 2  6 x  2 Simplify your answer.
Find the domain of y  f (x) where f is a polynomial, rational or root function.
30) Find the domain of each function. Write your answer in interval notation.
a) f ( x)  7 x  3
b) f ( x) 
7x
x  36
2
c) f ( x)  4 x  24
d) f ( x) 
9
x7
Solutions:
1) x  1.45, 1.16



2)
7, 5
21) y  1
3)
3, 13
22) y  
4)
 8,
 10
23) y  15x  41
5
3



7)


 9

,2
 3



2
 3
 2


26) (h, k )    , 2  , r = 3/2.
 9
 2


b) Not a function.

c)  f ( x)  2 x 2  5x  8
12)  , 8    7,  
d) f ( x  h)  2 x 2  4hx  2h2  5x  5h  8
29) a)
13)  0, 6 
14)  3, 0  ,  3, 0  ,  0, 9 
15) Intercepts are (16, 0), (0, 4), (0, 4) . The
graph is symmetric with respect to the x-axis.
16) The slope is 

28) a) f (2)  6 b) f ( x)  2 x 2  5x  8
11)   ,3 
3
2
17) The slope is undefined.
5
35
x y 
6
6
19) y  
x  32  y  4  25
27) a) Yes the relation is a function.
Domain: 3,4,5,6. Range 1,2,3.
10)   , 7 
2
18)
25)

8)  1, 5
9)
4
41
x
5
5
24) x 2  y 2  72
5)  , 2 
6) 7

20) x  8
3
11
x
2
2
b)
f ( x  h)  f ( x )
 5
h
f ( x  h)  f ( x )
 10 x  5h  6
h
30) a)  ,  
c)  6,  
b)  , 6    6, 6    6,  
d)  7,  