MENU
❌
Home
Math Forum/Help
Problem Solver
Practice
Algebra
Geometry
Tests
College Math
History
Games
MAIN MENU
1 Grade
Adding and subtracting up to 10
Comparing numbers up to 10
Adding and subtracting up to 20
Addition and Subtraction within 20
2 Grade
Adding and Subtracting up to 100
Addition and Subtraction within 20
3 Grade
Addition and Subtraction within 1000
Multiplication up to 5
Multiplication Table
Rounding
Dividing
Perimeter
Addition, Multiplication, Division
4 Grade
Adding and Subtracting
Equivalent Fractions
Divisibility by 2, 3, 4, 5, 9
Area of Squares and Rectangles
Fractions
Equivalent Fractions
Least Common Multiple
Adding and Subtracting
Fraction Multiplication and Division
Operations
Mixed Numbers
Decimals
Expressions
6 Grade
Percents
Signed Numbers
The Coordinate Plane
Equations
Expressions
Polynomials
Polynomial Vocabulary
Symplifying Expressions
Polynomial Expressions
Factoring
7 Grade
Angles
Linear Functions
8 Grade
Linear Functions
Systems of equations
Slope
Parametric Linear Equations
Word Problems
Exponents
Roots
Quadratic Equations
Vieta's Formulas
Progressions
Arithmetic Progressions
Geometric Progression
Progressions
Number Sequences
Reciprocal Equations
Logarithms
Logarithmic Expressions
Logarithmic Equations
Extremal value problems
Trigonometry
Numbers Classification
Geometry
Slope
Intercept Theorem
Law of Sines
Law of Cosines
Vectors
Probability
Limits of Functions
Properties of Triangles
Pythagorean Theorem
Matrices
Complex Numbers
Inverse Trigonometric Functions
Analytic Geometry
Analytic Geometry
Circle
Parabola
Ellipse
Conic sections
Polar coordinates
Integrals
Integrals
Integration by Parts
Home
Practice
Linear Functions
Linear Functions: Problems with Solutions
Problem 1
The proportional relation between distance traveled and the amount of time is shown in the following picture.
Which of the statements is true?
(A) The y coordinate of point A represents the distance traveled in 4 hours.
(B) The distance traveled in 1 hour is 60 kilometres.
(C) It is impossible to determine the distance if we have traveled zero hours.
(D) None of these is correct.
Solution:
Answer: (D) No answer is correct.
Point A has coordinates $(5, 400)$. It means that for 5 hours we travel 400 km.
Problem 2
The graph visualize an emplolyee pay based on his working hours.
Determine the rate per hour.
Solution:
The $x$ axis shows hours and $y$ axis the pay.
The point $(1,40)$ shows that if he works one hour he will be paid \$40.
The point $(2,80)$ shows that if he works 2 hours he will be paid \$80.
To know the payments per hour, we must measure the vertical distance between the points $(1,40)$ and $(2,80)$.
Distance $=y_{2}-y_{1} = 80-40$
The payment is 40 dollars per hour.
Problem 3
The following graph shows the relation between the distance traveled by a taxi and the total cost of the service.
Which of the following about the point A is true?
(A) A taxi service of 8 km has a cost of \$5
(B) A taxi service of 20 km has a cost of \$8
(C) A taxi service of 8 km has a cost of \$20
(D) None is correct.
Solution:
Correct: (B) A taxi service of 20 km has a cost of \$8.
The point A $(20, 8)$ shows that the cost of the taxi service of 20 kilometers is 8 dollars.
Problem 4
The following table represents the relation between x, y.
May this table represent a function?
X
Y
5
8
10
13
15
18
20
23
21
24
25
28
Yes
No
Solution:
The definition of a function is the following:
For each point of the starting set corresponds exactly one value of the arrival set. In the table this condition is met, for every value of x there are no two different values of y, therefore this table represents a function that relates the variable x, y.
Problem 5
Which of these relations is a function?
A
B
-1
0
-1
1
0
3
0
2
1
4
2
2
A
B
-1
0
-1
0
0
3
0
3
1
4
2
2
X
Y
5
10
15
15
20
25
25
35
25
24
25
28
(A) TABLE I and TABLE II
(B) TABLE I and TABLE III
(C) TABLE II and TABLE III
(D) None of these is correct.
Solution:
Answer: (B) TABLE I and TABLE III
The definition of a function is the following:
for every point of the first set corresponds a single value of the second set.
In table 1 the points $(-1,0)$ and $(-1,1)$ do not satisfy this condition, because when $x=-1$ there are two different values of $y$, also in table III, the points $(25,24)$ and $(25,28)$ do not meet the definition of a function.
Problem 6
Which of these relations is a function?
X
Y
5
5
10
10
15
15
20
20
21
21
25
25
X
Y
5
5
10
5
15
5
20
5
21
5
25
5
(A) TABLE I and TABLE II
(B) TABLE I
(C) TABLE II
(D) None of them.
Solution:
Both tables represent functions. In the first case we see the function identity to each value of x, the same value of y corresponds to it, this function is called identity function. In the second table we have the constant function, to all the values of x corresponds the same value of y, in both cases we have a function.
Problem 7
Let A and B be sets with elements:
$A=\left\{ 1,3,5,6,8\right\}$ $B=\left\{ a,b,d,f\right\} $
Is the set of ordered pairs a function or a relation between the sets A, B?
$R=\left\{ (1,b);(3,d);(6,f)\right\} $
Yes
No
Solution:
For each element of $x$ corresponds a single element of $y$, for this reason the set of ordered pairs represents a function from set $A$ to set $B$
Problem 8
Does the point $(1,3)$ belong to the graph of the function $y=2x-1$ ?
Yes
No
Solution:
In the linear function $y=2x-1$ we must substitute the value of $x$ by 1. $y=2(1)-1\Longrightarrow y=1$
Note that the graph of the function passes through the point $(1,1)$, but does not go through the point $(1,3$. Then we can conclude that the point $(1,3)$ does not belongs to the graph of the function $y=2x-1$
Problem 9
Which of the points $(1,3)$, $(0,3)$, $(2,0)$, $(0,2)$, do not belong to the graph of the function $y=x+2$?
(A) $(1,3)$ and $(0,3)$
(B) $(1,3)$ and $(0,2)$
(C) $(0,3)$ and $(2,0)$
(D) all points belong to the graph
Solution:
The correct answer is (B) $(1,3)$ and $(0,2)$.
$y=(1)+2 = 3 $ and
$y=(0)+2 =2$
So the the points $(1,3)$ and $(0,2)$ belongs to the graph of the function $y=x+1$.
You can check that none of the other points belong to the graph.
Problem 10
Given the function $y=3x-\frac{2}{5}$. Evaluate the function at x = 5.
(A) $\frac{5}{3}$
(B) $\frac{6}{5}$
(C) $\frac{3}{2}$
(D) $\frac{73}{5}$
Solution:
We must replace x by 5 in the definition of the function $y=3x-\frac{2}{5}$
$y=3(5)-\frac{2}{5}=15-\frac{2}{5}=\frac{75-2}{5}=\frac{73}{5}$
Problem 11
If $y=\frac{2x-1}{3}$, what is the value of $y$ when $x=1$?
$\frac{2}{3}$
$1$
$\frac{1}{3}$
$\frac{4}{3}$
Solution:
We must replace x by 1
$y=\frac{2(1)-1}{3}=\frac{1}{3}$
Problem 12
Which of following ordered pairs satisfy the function $y=5x-2$ ?
(A) $(0,-2)$ and $(1,3)$
(B) $(1,3)$ and $(0,2)$
(C) $(5,2)$ and $(2,5)$
(D) None of them
Solution:
Correct answer: (A) $(0,-2)$ and $(1,3)$
We must check if in the function $y=5x-2$ we replace x by 0 we get $y=-2$ and
if we replace x by 1 we get $y=3$.
For x = 0 we get
$y=5(0)-2 = 0-2 =-2$. So the the point $(0,-2)$ satisfies the function $y=5x-2$
and also $y=5(1)-2=5-2=3$ which shows that the point $(1,3)$ satisfies the function.
Submit a problem on this page.
Problem text:
Solution:
Answer:
Your name(if you would like to be published):
E-mail(you will be notified when the problem is published)
Notes
: use [tex][/tex] (as in the forum if you would like to use latex).
Correct:
Wrong:
Unsolved problems:
Contact email:
Follow us on
Twitter
Facebook
Author
Copyright © 2005 - 2020.