Question

NEED HELP WITH THESE 5 QUESTIONS!!!

#1 The graph shows a journey in a car. Which of the statements most likely describes the journey at the portion of the graph labeled K?

A line graph is drawn on the first quadrant of a coordinate plane. The x axis is labeled Time in seconds, and the y axis is labeled Distance in miles. The line graph is divided into 7 segments labeled I, J, K, L, M, N, and O. I starts at the origin and is a straight line slanting up. J is a line segment that starts at the end of I and is horizontal. K is a curve that starts at the end of J and curves up. L is a straight line that starts at the end of K and is horizontal. M is a straight line that starts at the end of L and slopes down. N is a straight line that starts at the end of M and is horizontal. O is a curve that starts at the end of N and curves down to finally touch the x axis.

The car travels the same distance per unit of time because the portion shows a linear, increasing function.
The car travels different distances per unit of time because the portion shows a linear, increasing function.
The car travels different distances per unit of time because the portion shows a nonlinear, increasing function.
The car travels the same distance per unit of time because the portion shows a nonlinear, increasing function.

#2 he graph below plots a function f(x):

graph of line segment going through ordered pairs 0,150 and 3, 0

If x represents time, the average rate of change of the function f(x) in the first three seconds is ___.

#3 The tables below show the values of y corresponding to different values of x:


Table A
x 3 3 2
y 1 0 0
Table B
x 3 5 5
y −2 2 −2


Which statement is true for the tables?
Both Table A and Table B represent functions.
Both Table A and Table B do not represent functions.
Table A does not represent a function, but Table B represents a function.
Table A represents a function, but Table B does not represent a function.

#4 What is the slope of the line that passes through (3, −7) and (−1, 1)?

Undefined
0
−2
2

#5 State the domain of the relation.

Discrete graph defined on the set of points negative two comma negative four and zero comma zero and positive one comma positive one and positive two comma positive two and positive three comma positive one and positive four comma positive six.

{−2, 0, 1, 2, 3, 4}
{−4, 0, 1, 2, 6}
{0, 1, 2, 3}
{−2, 4}

Answer 1

1)

Option: C is correct.

( The car travels different distances per unit of time because the portion shows a nonlinear, increasing function ).

As the graph is a curve so the distance traveled is different at different times also it is given that the curve is up.

2)

The graph below plots a function f(x):

graph of line segment going through ordered pairs (0,150) and (3, 0 ).

The rate of change of the function f(x) is given as:

`(f(3)-f(0))/(3-0)\\\\=(0-150)/(3)\\\\=-50`

The average rate of change of the function in first three seconds is: -50.

3)

Table A

x 3 3 2

y 1 0 0

Table B

x 3 5 5

y −2 2 −2

The correct statement is:

Both Table A and Table B do not represent functions.

( Because a function is a relation such that every element has a unique image.

In table A: 3 has two images or we can say y-value (1 and 0)

similarly in Table B: 5 has two values (2 and -2) )

4)

What is the slope of the line that passes through (3, −7) and (−1, 1)?

We know that the equation of the line in slope intercept form is given as:

y=mx+c where m represents the slope and c represents the y-intercept.

The equation of line passing through two points (a,b) and (c,d) is given by:

`y-b=(d-b)/(b-a)* (x-a)`

Here we have (a,b)=(3,-7) and (c,d)=(-1,1)

hence equation of line is:

`y-(-7)=(1-(-7))/(-1-3)* (x-3)\\\\y+7=(8)/(-4)* (x-3)\\\\y+7=-2* (x-3)\\\\y+7=-2x+6\\\\y=-2x+6-7\\\\y=-2x-1`

Hence the slope of line is: -2.

5)

The domain of the graph are the possible values where the function is defined.

Now here we are given graph of a relation as:

Discrete graph defined on the set of points negative two comma negative four and zero comma zero and positive one comma positive one and positive two comma positive two and positive three comma positive one and positive four comma positive six.

in table form we can write it as:

x -2 0 1 2 3 4

y -4 0 1 2 1 6

Hence the domain is the set of x-values.

i.e. domain is:

{-2,0,1,2,3,4}.

Answer 2

The car travels different distances per unit of time because the portion shows a nonlinear, increasing function; -50; Both Table A and Table B do not represent functions; −2 ; {−2, 0, 1, 2, 3, 4}

Explanation:

A linear graph of any sort is a graph that has a constant rate of change. This graph is not linear; therefore it does not have a constant rate of change. This means that the car travels different distances per unit of time between sections.

To find the rate of change, we find the slope between these two points. We use the formula

`m=(y_2-y_1)/(x_2-x_1)`

Using our points, we have

`m=(150-0)/(0-3)=(150)/(-3)=-50`

A function is a relation in which each element of the domain (x) is mapped to only one element of the range (y). In both of these tables, we have x-values that are mapped to two y-values; in Table A, 3 is mapped to 1 and 0; and in Table B, 5 is mapped to 2 and -2.

We use the slope formula again:

`m=(y_2-y_1)/(x_2-x_1)`

Using our points, we have

`m=(-7-1)/(3--1)=(-7-1)/(3+1)=(-8)/(4)=-2`

The domain of a graph is the set of inputs or x-values. From our points, we have the set:

{-2, 0, 1, 2, 3, 4}