Question

Let t(x)=-2x^3+5x-7. Find the new function for t(x) under the following transformations. Express t(x) as a cubic polynomial in the form ax^3+bx^2+cx+d.

A. Shift t(x) up 7 units and left 5 units
B.Reflect t(x) across the y-axis
c. Stretch t(x) horizontally so that it is twice as wide as the original function.

Answer 1

please help lol

Answer 2

to shift the function up 7 units add 7 to t(x)

the rule to shift a function a units to the left is

f(x) ----> f(x+a)

so for t(x) you replace each each x by x + 5 and simplify

Answer 3

So i'll start you off with A:-

adding 7 we get
-2x^3 + 5x - 7 + 7
= -2x^3 + 5x

Now replace the x by x + 5 and express it in the form required in the question.

Answer 4

2(x+5)^3+5(x+5). =2x^3+30x^2+155x+275

Answer 5

I just simplified it

Answer 6

looks good

Answer 7

is that the answer?

Answer 8

thats the answer to A

Answer 9

B when x is reflected acros the y axis the y values stay the same but the x values change to -x.
So if you replace each x by -x in -2x^3 + 5x - 7 you have the answer to B

Answer 10

* when f(x) is reflected

Answer 11

- I should have said t(x)!

Answer 12

so its just 2x^3-5x-7?

Answer 13

yeah

Answer 14

C:- for a horizontal stretch of twice the width you multiply the whole function by 1/2

Answer 15

the original function correct?

Answer 16

OH Hold on I'm not sure about that
I'll check that out.

Answer 17

oh ok lol

Answer 18

I was wrong you need to replace the x by 0.5x then simplify

Answer 19

so we have -2(0.5x)^3 + 5(0.5x) - 7

Answer 20

lol my brains dead. been up since 11 at night. ok so -.25^3+2.5x-7?

Answer 21

lol
sorry
You are correct

Answer 22

oh lol so is that it?

Answer 23

Yes
I have assumed that the 3 transformations are done on the original t(x) . Not consecutive. The question does not make that clear.

Answer 24

oh ok thank you so much. you mind helping me out on organizing the quadratic formula?

Answer 25

ok

Answer 26

12x+13-5x^2
I have it as -12+-sqrt12^2-4(-5)13 all over 2(-5)

Answer 27

that's correct

Answer 28

yes however I cannot seem to get the answer.

Answer 29

I just want to simplify it

Answer 30

work out the stuff thats in the brackets first
12^2 - 4*-5*13 = 144 + 260 = 404

Answer 31

so we have (-12 +/- sqrt 404 ) / -10

Answer 32

perhaps you may assist someone else right now. I have to go to the restroom for an emergency lol ill be right back

Answer 33

\(\Huge\color{#EB00FF}{\text{WELCOME}}\) \(\Huge\color{blue}{\text{TO}}\) \(\Huge\color{green}{\text{OPEN}}\)\(\Huge\color{purple }{\text{ STUDY!!!!!!!!!!!}}\) \(\Huge\heartsuit\)
may u plz close this