Multiple Transformations of Functions

Click For Summary
SUMMARY

The discussion centers on transforming the function f(x) = x³ into a new function through specific shifts and a stretch. The transformation involves a horizontal shift of 3 units to the right and a vertical shift of 1 unit upwards, resulting in the equation f(x) = a(x - 3)³ + 1. The constant 'a' represents the vertical stretch. Using the point (4, 1.5), participants are tasked with determining the value of 'a' to complete the transformation.

PREREQUISITES
  • Understanding of function transformations, including horizontal and vertical shifts.
  • Familiarity with cubic functions and their properties.
  • Knowledge of how to manipulate function equations to reflect transformations.
  • Experience with graphing tools like Desmos for visualizing transformations.
NEXT STEPS
  • Calculate the value of 'a' using the point (4, 1.5) in the equation f(x) = a(x - 3)³ + 1.
  • Explore the effects of different values of 'a' on the graph of the transformed function.
  • Learn about other types of transformations, such as reflections and compressions.
  • Investigate how to apply transformations to other types of functions, such as quadratic or exponential functions.
USEFUL FOR

Students studying algebra, educators teaching function transformations, and anyone interested in understanding the graphical representation of cubic functions.

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: 115
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: 109

Similar threads

Undergrad Transformation of Functions: How Do Domain and Range Change?
  • · Replies 4 ·
Replies
4
Views
2K
High School Correlation between shifting graph of a function and shifting the axes
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad My attempt to understand horizontal transformations of functions
  • · Replies 6 ·
Replies
6
Views
2K
MHB The shifting of h in vertex form
  • · Replies 1 ·
Replies
1
Views
2K
MHB Pre-calculus Grade 11 IB (higher level)
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Name of distance to nearest multiple of n function?
  • · Replies 1 ·
Replies
1
Views
1K
MHB Consecutive vertical and horizontal transformations of a function
  • · Replies 2 ·
Replies
2
Views
2K
Understanding the graphical effect of f(x+a)
  • · Replies 19 ·
Replies
19
Views
3K
Undergrad Order of transformation of functions?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Transforming coordinates between Cartesian and spherical
  • · Replies 1 ·
Replies
1
Views
2K