Answer:
g(x) = x²
The graph of g(x) is the same with the graph of f(x)
Step-by-step explanation:
* Lets explain how to solve the problem
- If the function f(x) reflected across the x-axis, then the new
function g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then the new
function g(x) = f(-x)
* Lets solve the problem
∵ The parent function f(x) = x² is represent by upward parabola
with vertex (0 , 0) (red graph in the attached picture)
∵ f(x) is reflected across the y-axis
- As the rule above reflection across the y-axis change the sign of x
∴ g(x) = f(-x)
∵ f(x) = x²
∴ g(x) = (-x)²
- Remember (-ve)^even number = (+ve)
∴ (-x)² = x²
∴ g(x) = x²
- The function g(x) is represent by upward parabola with vertex
(0 , 0) (black graph in the attached picture)
∴ The graph of g(x) is the same with the graph of f(x)
- The red graph and the black graph are coincide
Answer:
The cube of first six natural numbers are
1, 8, 27, 65, 125, 216
Step-by-step explanation:
Natural Numbers are known as 1, 2, 3, 4, ..., ∞
Now,
For Cube of first six natural numbers
1³ = 1
2³ = 8
3³ = 27
4³ = 64
5³ = 125
6³ = 216
Thus, The cube of first six natural numbers are
1, 8, 27, 65, 125, 216
<u>-TheUnknownScientist</u>
Answer:
![\frac{(18 + h) - 18}{(10 + h) - 10} = \frac{h}{h} = 1](https://tex.z-dn.net/?f=%5Cfrac%7B%2818%20%2B%20h%29%20-%2018%7D%7B%2810%20%2B%20h%29%20-%2010%7D%20%3D%20%5Cfrac%7Bh%7D%7Bh%7D%20%20%3D%201)
Step-by-step explanation:
Given: f(x) = x + 8
Interval: [10, 10 + h]
The function f(x) is an equation of a straight line and can also be expressed as;
y = x + 8
<em />
<em>*The slope in this case is equal to 1.</em>
∴ When x = 10 , y = 10 + 8 = 18
and,
When x = 10 + h , y = (10 + h) + 8 = 18 + h
Average rate of change is equivalent to the slope of the line but we should express it in terms of h.
So we are finding the rate of change from point (10, 18) to point (10 + h, 18 + h)
Slope = change in y ÷ change in x
i.e
Average rate of change or slope = ![\frac{(18 + h) - 18}{(10 + h) - 10} = \frac{h}{h} = 1](https://tex.z-dn.net/?f=%5Cfrac%7B%2818%20%2B%20h%29%20-%2018%7D%7B%2810%20%2B%20h%29%20-%2010%7D%20%3D%20%5Cfrac%7Bh%7D%7Bh%7D%20%20%3D%201)
Answer:
Only the mean increased.
Step-by-step explanation:
The mean is the total divided by the number of scores, and since adding 21 will increase the total score significantly, the mean increases.
The median is still 7.
The letters a and b becasue those are the first two letters