A set of ordered pairs, like the ones shown, represents a function only if each of the first coordinates is not repeated.
For example {(2, 5), (7, 8)} is a function, but {(2, 3), (6, 8), (2, -1)} is not because 2 is repeated.
We can check that each set of pairs we are given, are functions.
The inverses of each of these sets would be :
<span>{(–2, –1), (4, 0), (3, 1), (14, 5), (4, 7)} 4 repeats
{(2, -1), (4, 0), (5, 1), (4, 5), (2, 7)} 4 and 2 repeat
{(3, -1), (4, 0), (14, 1), (6, 5), (2, 7)} no repetition of 1st coordinates
{(4, -1), (4, 0), (2, 1), (3, 5), (1, 7)} 4 repeats
</span>
So only the inverse of <span>{(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} is also a function</span>
Answer:
1: linear
2: quadratic
3: exponential
4: cubic
5: linear
6: absolute value
7: quadratic
8: linear
9: exponential
10: linear
11: absolute value
Step-by-step explanation:
linear has the form y=mx + c whereby the highest power of x is 1.
Quadratic is a mathematical statement where the highest power of x is 2
Cubic is a mathematical statement where the highest power of x is 3
absolute value are literally in form of straight brackets
The equation gives the height of the ball. That is, h is the height of the ball. t is the time. Since we are looking for the time at which the height is 8 (h=8), we need to set the equation equal to 8 and solve for t. We do this as follows:
This is a quadratic equation and as it is set equal to 0 we can solve it using the quadratic formula. That formula is:
You might recall seeing this as "x=..." but since our equation is in terms of t we use "t-=..."
In order to use the formula we need to identify a, b and c.
a = the coefficient (number in front of)
= 16.
b = the coefficient of t = -60
c = the constant (the number that is by itself) = 7
Substituting these into the quadratic formula gives us:
As we have "plus minus" (this is usually written in symbols with a plus sign over a minus sign) we split the equation in two and obtain:
and
So the height is 8 feet at t = 3.63 and t=.12
It should make sense that there are two times. The ball goes up, reaches it's highest height and then comes back down. As such the height will be 8 at some point on the way up and also at some point on the way down.
Q.1.1
Q 1.2
this can't be simplified.
Q. 1.3
Q.1.4