anonymous
  • anonymous
Given the function f(x) = 3(x − 3)2 + 2, indicate the shifts that will affect the location of the vertex, and explain what effect they will have. Use complete sentences. •f(x+4) •f(x) + 4 •f(4x) •4•f(x)
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
so I believe that in the first it shifts it up, the second shifts it to the right. but I don't understand the last two....
anonymous
  • anonymous
@whpalmer4 can you please help
anonymous
  • anonymous
@ashy98

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

jchick
  • jchick
What happens if we add or subtract something from the result of a function?
anonymous
  • anonymous
I have no clue...
jchick
  • jchick
If we have f(x)=x, simple case, a straight line going through the origin and up and to the right with a slope of 1.
jchick
  • jchick
1 Attachment
anonymous
  • anonymous
so if you add or subtract something it will shift the line up and down?
jchick
  • jchick
Now let's add 1 to the function: y=f(x)+1=x+1 What does our new graph look like? What is the value of y at x=0? x=1, x=−3?
jchick
  • jchick
Yes, adding a positive value to the result translates the graph in the direction of positive y, and adding a negative value translates in the direction of negative y.
jchick
  • jchick
how do we shift right or left?
anonymous
  • anonymous
adding a positive or negative integer with in the parenthesis?
jchick
  • jchick
(-3,-3), (-2,-2), (-1, -1), (0,0), (1,1), (2,2), (3,3) that's the first line (-3,-2), (-2, -1), (-1, 0), (0, 1), (1,2), (2,3), (3,4) that's the second line
anonymous
  • anonymous
oh okay, that makes sense..
jchick
  • jchick
adding or subtracting from the argument of the function is to translate the graph to the left or the right.
anonymous
  • anonymous
0kay.. what happens when you multiply or divide from the function?
jchick
  • jchick
Do you have a guess?
anonymous
  • anonymous
I honestly didn't know you could before I saw this equation, so I have no clue what it will do to the graph..
jchick
  • jchick
you stretch or compress it
anonymous
  • anonymous
what does that mean?
jchick
  • jchick
if there is a function y=f(x) c*f(x) will stretch it vertically and f(x)/c will compress it vertically f(c*x) will compress it horizontally and f(x/c) will stretch it horizontally
jchick
  • jchick
Horizontal Changes A horizontal stretching is the stretching of the graph away from the y-axis. A horizontal compression is the squeezing of the graph towards the y-axis. If the original (parent) function is y = f(x), the horizontal stretching or compressing of the function is given by the function g(x), where g(x) = f(bx).
jchick
  • jchick
Vertical Changes A vertical stretching is the stretching of the graph away from the x-axis. A vertical compression is the squeezing of the graph towards the x-axis. If the original (parent) function is y = f(x), the vertical stretching or compressing of the function is given by the function g(x), where g(x) = bf(x).
jchick
  • jchick
Does that help?
anonymous
  • anonymous
so does that mean that the slope would change from say 1 to 1/ any number higher?
jchick
  • jchick
if 0 < b < 1 (a fraction), the graph is stretched horizontally by a factor of b units. if b > 1, the graph is compressed horizontally by a factor of b units. if b should be negative, the horizontal compression or horizontal stretching of the graph is followed by a reflection of the graph across the y-axis.
anonymous
  • anonymous
oh okay.. im understanding a little better.. so if x is anything greater than one it stretches and anything le than one it will compress?
jchick
  • jchick
. It affects where it reflects
jchick
  • jchick
Whether or not it is across the y or x axis
jchick
  • jchick
for instance in vertical If b should be negative, then the vertical compression or vertical stretching of the graph is followed by a reflection across the x-axis.
anonymous
  • anonymous
ahhh okay hats making a lot more sense to me.
anonymous
  • anonymous
now how does it affect the vertex?
jchick
  • jchick
You can see that the vertex moved from (3,2) to (−1,2)
jchick
  • jchick
And 3 - (-1)
anonymous
  • anonymous
oh yeah, so it moves the way the graph would?
jchick
  • jchick
Yes
jchick
  • jchick
So can you solve it from here?
jchick
  • jchick
f(x + 4) shifts the function to the left by 4 units, which results in the vertex shifting from (3,2) to (-1,2). (ii) f(x) + 4 shifts the function vertically by 4 units, which results in the vertex shifting to (3,6). (iii) The transformed function is g(x) = f(4x) = 3*(4x - 3)^2 + 2 = 48*(x - (3/4))^2 + 2, so the vertex shifts to ((3/4), 2). (iv) The transformed function is g(x) = 4*f(x) = 12*(x - 3)^2 + 8, so the vertex shifts to (3,8)
anonymous
  • anonymous
so the vertex moves the same as the graph , if you do f(x)+1 it move up unless negative, F(x+1) changes it to the right unless negative and multiplying with expand it while dividing will compress it? am I right?
jchick
  • jchick
Correct
anonymous
  • anonymous
oh okay thankyou. this has really helped me.
jchick
  • jchick
Your welcome!
jchick
  • jchick
Think of it this way with multiplication you will get a larger number than dividing
jchick
  • jchick
division makes things smaller
anonymous
  • anonymous
that makes it a little easier to understand,
jchick
  • jchick
Ok good

Looking for something else?

Not the answer you are looking for? Search for more explanations.