Question

Eva played her favorite video game for 14 hours last week. Today, Eva's parents restricted her to 4 hours each week for the next 7 weeks. Create the function, f(x), that models Eva's total video game time, and explain what each number in the situation represents graphically, using complete sentences.

Answer 1

@Loser66

Answer 2

Help Me

Answer 3

I need to create an F(x) function :(

Answer 4

You're looking for the total, so it'll be \(F(x)=new~ time ~allowed\times ~number ~of ~weeks+ old ~time~ allowed\times~ previous~ week\)

Answer 5

So \(\textsf{F(x)=4x+14}\)

Answer 6

Oh ok Thank u so much @DangerousJesse umm i have two more questios I hope u dont mind

Answer 7

That's fine :)

Answer 8

Pedro has created the function f(x) = the quantity of 4x minus 3, divided by 2 to represent the number of assignments he has completed, where x represents the number of weeks in the course. Pedro discovers that, using the inverse function to solve for x = 30, he can predict when he will have 30 assignments completed. Explain to Pedro how to accomplish this, using complete sentences.

Answer 9

@DangerousJesse

Answer 10

@phi

Answer 11

it's hard to read your equations when written out (which is why people invented the way we do it)
is it
\[ f(x) = \frac{4x-3}{2} \]
?

Answer 12

Yes

Answer 13

the technique to find the inverse function is write it as
\[ y = \frac{4x-3}{2} \]
then "swap x and y" to get
\[ x = \frac{4y-3}{2} \]
now "solve for y"

The first step is multiply both sides by 2
can you do that ?

Answer 14

2 x X = 4y - 3 / 2 x 2

Answer 15

is it like tha

Answer 16

almost. we leave out the multiply sign x (because it will be confused with the variable x)

so it would look like this
\[ 2x = \frac{4y-3}{2} \cdot 2 \]
when you have 2/2 (on the right side), that simplifies to 1, so you have
\[ 2x = 4y-3 \]
now add +3 to both sides. what do you get ?

Answer 17

2x = 4y - 3 would it be like this

+3 +3

Answer 18

ok,
but write it on one line
2x+3 = 4y-3 + 3

can you simplify the right side?

Answer 19

Ok would it be

5x = 4y - 6 Im kinda confsed im sorry

Answer 20

2x + 3 stays like that. You have 2 x's plus a 3

on the right side you have 4 y's , a 3 and take away a 3

Answer 21

Oh ok so then

2x + 3 = 4y

Answer 22

is that correct @phi

Answer 23

yes, much better

now divide both sides by 4:
\[ \frac{2x + 3 }{4}= \frac{4y }{4} \]

Answer 24

can you simplify the right side?

Answer 25

Ok so would it be

4 times 2x + 3 / 4 = 4y/4 times 4

Answer 26

we don't want to multiply both sides by 4.

Here is the idea: we want "y" by itself

when we have
\[ \frac{4y}{4}\]
that is the same as
\[ \frac{4}{4} \cdot \frac{y}{1} \]
If you multiply fractions, you multiply top time top and bottom times bottom
we would get back 4y/4

However, 4/4 is 1, so
\[ \frac{4}{4} \cdot \frac{y}{1} \\ 1 \cdot \frac{y}{1} \\
1\cdot y\\y
\]

Answer 27

in other words, the reason we divided 4y by 4 is to make it y (by itself)
to keep things even, we divide the other side by 4
we get
\[ \frac{2x+3}{4} = y\]

now you use this inverse function to answer the question.
replace x with 30
can you do that ?

Answer 28

ok

Answer 29

2(30) + 3 / 4 = y
60 + 3 / 4 = y
63 / 4 = y
15.75

Answer 30

yes. 15.75 is the number of weeks it will take to finish 30 assignments.

Answer 31

EEEKK THANK U SO MUCH :)

Answer 32

I hope you have time to review how to "solve" equations. The steps (once you learn them) are easy to do.