Math 110 Test 2 Practice
Sections 2.1–2.5
1. Write an equation for each line and then sketch the graph.
Label the x and y-intercepts.
(i) Slope = –2; containing the point (3,–1)
(ii) Slope = 0; containing the point (–5, 4)
(iii) Slope undefined; containing the point (–3,4)
(iv) x-intercept = 2; containing the point (4, –5)
(v) y-intercept = –2; containing the point (5,–3)
(vi) Containing the points (3,–4) and (2,1)
(viii) Perpendicular to x + y = 2 ; containing the point (4,–3)
2. Given the points P(7,4) and Q(–3,2). Find each of the following.
(i) The slope of the line containing P and Q. (ii) The length of the segment PQ.
(iii) The midpoint of the segment PQ.
3. Suppose that a graph contains the point (5, –3).
(i) If the graph has x-axis symmetry, give another point that must also be on the graph.
(ii) If the graph has y-axis symmetry, give another point that must also be on the graph.
(iii) If the graph has origin symmetry, give another point that must also be on the graph.
4. For each graph shown below, list the intercepts of the graph, and determine whether
the graph is symmetric with respect to the x-axis, the y-axis, and/or the origin.
5. For each equation, find the intercepts and test for symmetry.
3x
(i) x 2 = y
(ii) y = −5x (iii) 9x 2 + 4y 2 = 36 (iv) y = 2
x +9
(iv) y = x 2 + 16x + 60
6. Find the value of b so that the point ( b,2 ) is on the graph of the equation y = x 2 + 4x .
7. The cost of operating a car with 1000 miles on it is $122. The cost of operating a car
with 2000 miles on it is $244.
(i) Construct a linear equation that describes the relationship between the car’s
operating cost, in dollars, and the car’s mileage.
(ii) What is the operating cost of a car that has 1423 miles on it?
Math 110 Test 2 Practice
Sections 2.1–2.5
8. A cereal company finds that the number of people who will buy one of its products in
is linearly related to the amount of money it spends on advertising. If the company
spends $40,000 on advertising, then 100,000 boxes of cereal will be sold, and if it
spends $60,000 on advertising, then 200,000 boxes will be sold.
(i) Construct an equation describing the relation between the amount spent on
advertising and the number of boxes of cereal sold.
(ii) How much must be spent on advertising in order to sell 300,000 boxes of cereal?
9. For each circle equation, find the center and the radius, then graph the circle.
2
(ii) x 2 + y 2 − 2x + 4y = 0
(i) x 2 + ( y − 1) = 4
(iii) 5x 2 + 5y 2 − 30x + 60y = 0
10. Write the standard form of the equation with the given center and radius.
(i) Center (–2,3); radius = 4
(ii) Center (–4,–5); radius = 8
11. Find the domain of each function.
2x
(i)
f ( x) = 2
x − 49
(iii)
12.
f ( x) =
x +1
x−3
Use the given function graph to answer
the questions.
(ii)
f ( x ) = x 2 − 5x
(iv)
f ( x) =
x+5
x + 6x + 8
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
2
Domain:
Range:
x-intercept:
y-intercept:
f ( −4 ) =
f ( x ) = −3 when
f (x) > 0 when
Graph y = f ( x ) + 2 .
Graph y = f ( x + 1) .
Graph y = f ( −x ) .
Increasing on intervals:
Decreasing on intervals:
Discuss symmetry.
Is the function even, odd, or
neither?
Math 110 Test 2 Practice
Sections 2.1–2.5
For problems 13–16, start with the appropriate basic function graph and use transformations to
graph the given function. You must label at least 3 points on your
final graph. Also identify the domain, range, and intercepts of the final graph
13.
h ( x) = ( x − 2) + 1
14.
F ( x) = x − 3
15.
p ( x ) = −2 x − 4
16.
g ( x ) = 2 ( x + 1) + 1
17.
Suppose f is a linear function so that
f ( 3) = 6 and f ( 5 ) = −8 . Write the
formula for this function.
2
18.
3
Find the value of A if f ( x ) =
and f ( 3) = 1 .
9 − Ax
5x + 6
For questions 19–22, select the best answer choice.
(
)
19. If −2,9 is a point on the graph of y = f ( x ) , which of the following points must be
(
)
B. ( −4,49 )
on the graph of y = 5 f x − 2 + 4 ?
A.
(0,41)
(
)
C. −4,41
(
D. 0,49
)
20. The graph of the function y = f ( x ) shown on the left is transformed to yield the graph
shown on the right.
y = f ( x)
Choose the function formula that represents the transformed graph.
A. y = f ( x + 2 )
B. y = f ( x − 2 )
C. y = f ( x ) + 2
D. y = f ( x ) − 2
Math 110 Test 2 Practice
Sections 2.1–2.5
21. The graph of the function y = f ( x ) shown on the left is transformed to yield the graph
shown on the right.
y = f ( x)
Choose the function formula that represents the transformed graph.
1
1
A. y = −2 f ( x )
B. y = 2 f ( −x )
C. y = − f ( x )
D. y = f ( −x )
2
2
22. The graph of the function y = f ( x ) shown on the left is transformed to yield the graph
shown on the right.
y = f ( x)
Choose the function formula that represents the transformed graph.
1
A. y = −3 f ( x )
B. y = f ( −3x )
C. y = − f ( x )
D. y =
3
⎛ 1 ⎞
f ⎜ − x⎟
⎝ 3 ⎠
Math 110 Test 2 Practice
Sections 2.1–2.5
23. An open box is to be made by cutting out an identical square with sides equal x inches
from each corner of a rectangular piece of cardboard and turning up the sides (see the figure).
Express the volume V of the box as a function of x.
24. A rectangle is to be inscribed in a semi-circle. The semi-circle has a radius of 5.
Express the area of the rectangle as a function of the variable x shown in the
diagram.
25. Given the graph of the curve y = x and point P(5,0), express the distance
from the curve to point P as a function of x.