Which of the following functions are odd?
2 answers:
Answer:
Option 1, 2 and 3
Step-by-step explanation:
A function f(x) is odd if f(-x) = -f(x).
The graphs of odd functions are symmetric with the origin.
It is also known that the sum of two odd functions results in an odd function, so <em>the third option is an odd function.</em>
The first option shown is:
If we make f (-x) we are left with:
The function is odd.
The second option is a graph that has rotational symmetry of 180 ° with respect to the origin, that's why it is odd function.
The rest of the options are not odd functions because it is not true that f(-x) = -f(x)
Option 1 and 2 and 3
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Answer:
The graph of g(x) is stretched vertically by a factor of 5/3.
Step-by-step explanation:
f(x) = √x
g(x) = √25/9 x = 5/3 √x
5/3 > 1 .. vertical stretch by a factor of 5/3
Given:
Max's house has two steps on the front porch.
Size of each step is the same.
To find:
The total vertical distance covered by the two steps.
Solution:
From the given figure, it is clear that,
Base length of each step = 6 in
Hypotenuse = 10 in
Let h be the vertical height of each step.
Using Pythagoras theorem, the vertical height of one step is
Taking square root on both sides.
Height cannot be negative. So, h = 8 in.
Now,
Vertical height of 2 steps =
=
So, the total vertical distance covered by the two steps is 16 in.
Therefore, the correct option is A.