MHB Multiple Transformations of Functions

AI Thread Summary
To transform the function f(x) = x^3 into the new function, a horizontal shift of 3 units to the right and a vertical shift of 1 unit upward is required. The transformation can be expressed as f(x) = a(x-3)^3 + 1, where 'a' represents the stretch factor. Given the point (4, 1.5), the value of 'a' can be determined by substituting this point into the equation. This results in an equation that allows for the calculation of 'a', completing the transformation process. Understanding these transformations is crucial for accurately modifying the function.
saucybadimo
Messages
1
Reaction score
0
View attachment 9341

I have to transform the first function which is f(x)=x^3 to the second function. First, I have to find each shift then combine those to make a new function equation. I've used desmos and I know that there is a horizontal shift 3 units to the right. There is a vertical shift up but I don't know how many units. And I believe there is a stretch. There are only 3 transformations. PLEASE HELP!
 

Attachments

  • Screen Shot 2019-11-04 at 8.42.05 AM.png
    Screen Shot 2019-11-04 at 8.42.05 AM.png
    21.8 KB · Views: 104
Mathematics news on Phys.org
note the function center point $(0,0)$ is translated to $(3,1)$, a horizontal shift right 3 units and a vertical shift up 1 unit.

taking into account the horizontal & vertical shifts, we have ...

$f(x) = a(x-3)^3 + 1$

... where $a$ is the constant causing the stretch

using the point $(4,1.5)$, can you determine the value of $a$ ?
 

Attachments

  • cubic_transformation.jpg
    cubic_transformation.jpg
    47.3 KB · Views: 100

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »
Thread 'Video on imaginary numbers and some queries'

Thread 'Video on imaginary numbers and some queries'

Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
View full post »
Thread 'Unit Circle Double Angle Derivations'

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
View full post »

Similar threads

I Transformation of Functions: How Do Domain and Range Change?
Replies
4
Views
2K
B Correlation between shifting graph of a function and shifting the axes
Replies
5
Views
2K
I My attempt to understand horizontal transformations of functions
Replies
6
Views
2K
I Moving center of coordinates in the polar graph
Replies
2
Views
2K
MHB The shifting of h in vertex form
Replies
1
Views
1K
MHB Pre-calculus Grade 11 IB (higher level)
Replies
2
Views
2K
I Name of distance to nearest multiple of n function?
Replies
1
Views
1K
MHB Consecutive vertical and horizontal transformations of a function
Replies
2
Views
2K
I Get the time axis right in an inverse Fast Fourier Transform
Replies
2
Views
3K
Understanding the graphical effect of f(x+a)
Replies
19
Views
2K

Hot Threads

Recent Insights

Back
Top