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
-4 = 10 False.
Option B:
(-3 , 7.5)
g(x) = 2.5|x|
7.5 = 7.5 True.
Option C:
(-2 , 5.5)
5.5 = 2 False.
Option D:
(-1 , -2.5)
-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)
Answer:
We conclude that the person is saving $60 dollars per week.
Hence, option C is true.
Step-by-step explanation:
Given the table chart
Week Saving Money
2 60
4 120
6 180
8 240
We know to determine the slope to find the rate of change.
Taking the points (2, 60) and (4, 120)
Rate of change = Slope = [y₂ - y₁] / [x₂ - x₁]
= [120 - 60] / [4 - 2]
= 60 / 2
= $30 dollars per week
Now, taking the points (4, 120) and (6, 180)
Rate of change = Slope = [180 - 120] / [6 - 4]
= [60] / [2]
= $30 dollars per week
Now, taking the points (6, 180) and (8, 240)
Rate of change = Slope = [240 - 180] / [8 - 6]
= [60] / [2]
= $30 dollars per week
- This concludes that the rate of change is contant i.e. $30 dollars per week
Therefore, we conclude that the person is saving $60 dollars per week.
Hence, option C is true.