PSAT Math : Algebraic Functions
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Example Questions
Example Question #336 : Algebra
If 
Solve this problem using picked numbers. Choose an odd number to represent 
Substitute into each equation to find the correct answer:
This number is even, and likely the answer we are looking for. Just in case, quickly check the other answers to make sure no others come out even.
This expression gives an odd answer and must be incorrect.
This expression gives an odd answer and must be incorrect.
This expression gives an odd answer and must be incorrect.
This expression gives an odd answer and must be incorrect.
Only the first answer is even. The answer is 
Example Question #72 : Algebraic Functions
If 
What is 
To find f(4), input a 4 in every place you see an x in the equation. That gives you
When you simplify this expression, you get
When you add together each part, you get
Example Question #16 : Algebraic Functions
What is the value of the function f(x) = 6x2 + 16x – 6 when x = –3?
–12
96
–108
0
0
There are two ways to do this problem. The first way just involves plugging in –3 for x and solving 6〖(–3)〗2 + 16(–3) – 6, which equals 54 – 48 – 6 = 0. The second way involves factoring the polynomial to (6x – 2)(x + 3) and then plugging in –3 for x. The second way quickly shows that the answer is 0 due to multiplying by (–3 + 3).
Example Question #17 : Algebraic Functions
Given the functions f(x) = 2x + 4 and g(x) = 3x – 6, what is f(g(x)) when x = 6?
12
144
16
28
192
28
We need to work from the inside to the outside, so g(6) = 3(6) – 6 = 12.
Then f(g(6)) = 2(12) + 4 = 28.
Example Question #71 : Algebraic Functions
A function f(x) = –1 for all values of x. Another function g(x) = 3x for all values of x. What is g(f(x)) when x = 4?
–3
3
–12
12
–1
–3
We work from the inside out, so we start with the function f(x). f(4) = –1. Then we plug that value into g(x), so g(f(x)) = 3 * (–1) = –3.
Example Question #19 : Algebraic Functions
What is f(–3) if f(x) = x2 + 5?
15
14
–4
4
–14
14
f(–3) = (–3)2 + 5 = 9 + 5 = 14
Example Question #21 : Algebraic Functions
For all values of x, f(x) = 7x2 – 3, and for all values of y, g(y) = 2y + 9. What is g(f(x))?
14y2 + 3
14x2 + 3
14x2 – 3
2x + 9
7y2 – 3
14x2 + 3
The inner function f(x) is like our y-value that we plug into g(y).
g(f(x)) = 2(7x2 – 3) + 9 = 14x2 – 6 + 9 = 14x2 + 3.
Example Question #35 : Algebraic Functions
Find
Simply plug 6 into the equation and don't forget the absolute value at the end.
absolute value = 67
Example Question #72 : Algebraic Functions
An outpost has the supplies to last 2 people for 14 days. How many days will the supplies last for 7 people?
Supplies are used at the rate of 
Since the total amount of supplies is the same in either case, 
Solve for days to find that the supplies will last for 4 days.
Example Question #73 : Algebraic Functions
Worker 
The rates are what needs to be added. Rate 
Now invert the equation to get back to hours per trinket, which is what the question asks for:
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