Answer:
Option B is correct.
The point which lies on the new graph g(x) is, (-3, 7.5)
Step-by-step explanation:
For a base function f(x), a new function g(x) = cf(x) is vertically stretched by a factor c if c> 1.
Given the parent function: f(x) =|x|
Now, by vertically stretched definition,
A function f(x) is vertically stretched by a factor of 2.5 then; we have the new function or new graph i.e,
g(x) = 2.5 f(x) where c=2.5 > 1
therefore, g(x) =2.5|x|
We have to find which point lies on the new graph;
Option A:
(-4 , -4)
Here x = -4 and g(-4) = -4
[tex]g(-4) = 2.5 |-4|[/tex]
[tex]-4=2.5 \cdot 4=10[/tex]
-4 = 10 False.
Option B:
(-3 , 7.5)
g(x) = 2.5|x|
[tex]g(-3) = 2.5 |-3|[/tex]
[tex]7.5= 2.5 \cdot 3=7.5[/tex]
7.5 = 7.5 True.
Option C:
(-2 , 5.5)
[tex]g(-2) = 2.5 |-2|[/tex]
[tex]5.5 = 2.5 \cdot 2=5[/tex]
5.5 = 2 False.
Option D:
(-1 , -2.5)
[tex]g(-1) = 2.5 |-1|[/tex]
[tex]-2.5 = 2.5 \cdot 1=2.5[/tex]
-2.5 = 2.5 False
Therefore, from above you can see that the only point which is true for the new graph is, (-3 , 7.5)
