Question

Consider the following function.

Answer 1

\[q(x) = \frac{ 9 }{ 7x }\]

Find two points on the graph of this function, other than the origin, that fit within the given [−10,10] by [−10,10] grid. Express each coordinate as an integer or simplified fraction, or round to four decimal places as necessary.

Answer 2

Is there a graph?

Answer 3

you just need to pick any two x-values (besides 0, since the origin is excluded) between -10 and 10, plug in the value into the function, find the value of the function, and plot the two points

Answer 4

-6

Answer 5

@lowkey @vocaloid

Answer 6

ok, so plug x = -6 into the function

Answer 7

\[q(x) = \frac{ 9 }{ 7(-6)}\]

Answer 8

could -6 be the right number ?

Answer 9

could -6 be the right number ?

Answer 10

yes, because x -6 is between -10 and 10

keep simplifying 9/7(-6)

Answer 11

\[-\frac{ 54 }{ 7}\]

Answer 12

6 is in the denominator. you do not multiply 9 by -6 because 9 is in the numerator.

notice how 9 and 6 have a common factor (3). so factor out 3 from both 9 and 6.

Answer 13

alternatively, you could just plug 9/(7(-6)) into a calculator and convert it to a decimal (round to 4 digits), because the problem accepts decimals as answers

Answer 14

-0.21428571428

Answer 15

good just be sure to round to 4 digits

repeat this process with some other x-value

Answer 16

okay , what do i put for both sides on the first

Answer 17

you plugged in x = -6 and got q(x) = -0.2143, so (-6,-0.2143)

Answer 18

alright and how about -3

Answer 19

sure

Answer 20

9/7(-3)

Answer 21

-3.85714285714

Answer 22

you need to divide by -3, not multiply

Answer 23

-0.42857142857

Answer 24

good, round to 4 digits, enter the coordinate

Answer 25

-0.4286

Answer 26

-3, -0.4286

Answer 27

good

Answer 28

notice the conditions for the function:

first row applies for x < -2
second row applies for x >= 5

f(1) means x = 1

does x = 1 meet either of the function conditions? is x = 1 less than -2 or greater than 5?

Answer 29

less than -2

Answer 30

1 is not less than -2

because x = 1 does not meet either condition, f(1) is undefined

Answer 31

oh sorry

Answer 32

Evaluate this function at x=5. Express your answer as an integer or simplified fraction. If the function is undefined at the given value, indicate "Undefined".

Selecting a radio button will replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered answer is used.

f(5) = ____________ Undefined

Answer 33

this time, since you have f(5), x = 5 which meets the conditions in the second row (x >=5) so plug x = 5 into the second row of the function

Answer 34

-3(5) - 3

Answer 35

good, keep simplifying

Answer 36

-18

Answer 37

good

Answer 38

Evaluate this function at x=−5. Express your answer as an integer or simplified fraction. If the function is undefined at the given value, indicate "Undefined".

Selecting a radio button will replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered answer is used.

f(-5) = ____________ Undefined

Answer 39

notice how x = -5 meets the first condition (x < -2) so you'd use the first row

Answer 40

okay

Answer 41

-5^2 + -5 - 2

Answer 42

good just be careful with your signs, if you want -5 squared you need to enter (-5)^2

keep simplifying

Answer 43

(-5)^2 + -5 - 2

Answer 44

18

Answer 45

good