Question

7.   Find the range of the function f(x) = 4x – 1 for the domain {–1, 0, 1, 2, 3}.  (1 point)

Answer 1

Answer:

Ques 7)    

{–5, –1, 3, 7, 11}

Ques 8)

3

Ques 9)

one solution.

Ques 10)

(2,-3)

Ques 11)

y= -2x+3

Step-by-step explanation:

Ques 7)

We have to find the range of the function:

f(x)=4x-1.

Given that domain is:

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

The range of the function is the value of the function corresponding to the points of the domain.

so when x= -1

f(x)=4×(-1)-1=-4-1=-5

when x=0

f(x)=4×0-1=0-1=-1

when x=1

f(x)=4×1-1=4-1=3

when x=2

f(x)=4×2-1=8-1=7

when x=3

f(x)=4×3-1=12-1=11

Hence, the range of the function is:

{-5,-1,3,7,11}

Ques 8)

We have to find the slope of the graph of the equation:

$9x-3y=15$

Firstly we will write our equation in the slope intercept form as:

$y=mx+c$

Where m is the slope of the graph and c is the y-intercept of the graph.

Hence,

$9x-15=3y\\\\3y=9x-15\\\\y=\dfrac{9x-15}{3}\\\\y=\dfrac{9}{3}x-\dfrac{15}{3}\\\\y=3x-5$

Hence, the slope of the equation is:

3

Ques 9)

We have to find the  number of  solution of the system of equations as:

x – 2y = 2  

y = –2x + 5

On solving the system of equation by substitution method:

we put second equation in first to obtain:

x-2(-2x=5)=2

x+4x-10=2

5x=2+10

5x=12

x=12/5=2.4

Also putting the value of x in second equation we obtain:

y=0.2

Hence, we obtain a unique value of x and y on solving these system of equations.

So it has only one solution.

Ques 10)

We are given system of equation as:

3x-5y=21

2x+y=1

the second equation could also be written as:

y=1-2x-----------(a)

on putting the value of y in first equation we get:

3x-5(1-2x)=21

3x-5+10x=21

13x-5=21

13x=21+5

13x=26

x=26/13=2

i.e. x=2

on putting the value of x in equation (a) we get:

y=1-2×(2)=1-4=-3

i.e. y= -3

Hence the solution is:

(2,-3)

Ques 11)

We have to convert the equation:

4x+2y=6 into slope-intercept form of the line.

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

y=mx+c

where m is the slope of the line and c is the y-intercept.

2y=-4x+6

on dividing both side of the equation by 2 we obtain:

y=-2x+3

Answer 2

7. {-5, -1, 3, 7, 11}
8. 3
9. one solution
10. (2, -3)
11. 7=2x+3