The first one is false. Functions can also be other shapes, like parabolas or exponential.
The second is true. If x is 2 then y is also 2.
ANSWER
EXPLANATION
It was given that:
and
Perform the scalar multiplication to obtain:
We add the corresponding components to get;
The first choice is correct.
1 hr = 60 minutes
15 minutes x _4_= 60 min
10 flights x 4 = 40 flights
Answer: 40 flights per hour
That perpendicular line will have slope , negative reciprocal to the slope of this line:
x +9y - 2 = 0 and its slop is - 1/9 { 9y = - x - 2 → y = (-1/9 )x - 2/9 }
So the slope of the perpendicular line will be ? 9
There fore the equation of the perpendicular line : y = 9x + b
“b” to be found by using other conditions
x intercept for this line ( put y = 0 ): -b/9
x intercept for 2x - 9y + 27 = 0 ( put y = 0) : - 27/2
Just equate the two: -b/9 = -27/2 → b = 243/2
y = 9x + 243/2
Problem 7
x is the number of tickets and f(x) is the cost of those x tickets. So if you wanted say 2 tickets, then you would plug x = 2 into the f(x) function to find the cost it would take to get those 2 tickets.
The inverse function reverses all this. If we have the cost in mind, then we can use the inverse to determine how many tickets cost that dollar amount. Since everything swaps, this means x is now the cost in dollars and f^(-1)(x) is the number of tickets. Problem 8 below explains this in more detail while also going over an example.
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Problem 8
You should find back in problem 6 that the inverse function is
f^(-1)(x) = (x-12)/44
Let's plug in x = 320
f^(-1)(x) = (x-12)/44
f^(-1)(320) = (320-12)/44 ... replace x with 320
f^(-1)(320) = 308/44
f^(-1)(320) = 7
So x = 320 leads to f^(-1)(x) = 7
Meaning that if you have a budget of $320, then you can buy at most 7 tickets. Or if you want to spend exactly $320, then you need to buy 7 tickets.
Back in problem 5, the f(x) function you should have gotten was f(x) = 44x+12
Let's plug in x = 7 and see what happens
f(x) = 44x+12
f(7) = 44*7+12
f(7) = 308+12
f(7) = 320
So this shows that 7 tickets cost $320, which is the reverse of what we got earlier. Which is expected because the inverse swaps everything.
So in summary, f^(-1)(320) = 7 tells the reader "if you want to spend $320, then you need to get 7 tickets". In a sense, it is the same as solving 44x+12 = 320 for x to get x = 7.