Functions can be transformed from one form to another
- The relationship between f(x) and g(x) is that: f(x) was translated 3 units left, vertically stretched by 2 and the shifted 4 units down.
The attributes of f(x) are:
- [tex]\mathbf{Domain = (-\infty, \infty)}[/tex]
- [tex]\mathbf{Range = [0, \infty)}[/tex]
- [tex]\mathbf{Intercepts = 0}[/tex]
The attributes of g(x) are:
- [tex]\mathbf{Domain = (-\infty, \infty)}[/tex]
- [tex]\mathbf{Range = [-4, \infty)}[/tex]
- [tex]\mathbf{x-intercepts = -5,-1}[/tex]
- [tex]\mathbf{y-intercept = 2}[/tex]
The functions are given as:
[tex]\mathbf{f(x) = |x|}[/tex]
[tex]\mathbf{g(x) = 2|x+3|-4}[/tex]
(a) Changes from f(x) to g(x)
See attachment for the graphs of f(x) and g(x)
From the graph, we have the following observations
- f(x) is shifted left by 3 units
- Then vertically stretched by a factor of 2
- Lastly, the function is shifted down by 4 units to create g(x)
(b) Key attributes of f(x) and g(x)
Using the graph as a reference, the attributes of f(x) are:
[tex]\mathbf{Domain = (-\infty, \infty)}[/tex] --- because the graph extends in both directions of the x-axis
[tex]\mathbf{Range = [0, \infty)}[/tex] --- because the y-coordinates start at 0, and the graph opens upward
[tex]\mathbf{Intercepts = 0}[/tex] ---- the x and the y intercept is 0, because the graph passes through (0,0)
The attributes of g(x) are:
[tex]\mathbf{Domain = (-\infty, \infty)}[/tex] --- because the graph extends in both directions of the x-axis
[tex]\mathbf{Range = [-4, \infty)}[/tex] --- because the y-coordinates start at -4, and the graph opens upward
[tex]\mathbf{x-intercepts = -5,-1}[/tex] ----because the graph crosses the x-axis at -5 and -1
[tex]\mathbf{y-intercept = 2}[/tex] ----because the graph crosses the y-axis at 2
Read more about graphs at:
https://brainly.com/question/9125219
