SAT Math : Algebraic Functions
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Example Question #1 : How To Find F(X)
For all positive integers, let k* be defined by k* = (k-1)(k+2) . Which of the following is equal to 3*+4*?
5*
7*
6*
4*
5*
We can think of k❋ as the function f(k)=(k-1)(k+2), so 3❋+4❋is f(3)+f(4). When we plug 3 into the function, we find f(3)=(3-1)(3+2)=(2)(5)=10, and when we plug 4 into the function, we find f(4)=(4-1)(4+2)=(3)(6)=18, so f(3)+f(4)=10+18=28. The only answer choice that equals 28 is 5❋ which is f(5)=(5-1)(5+2)=(4)(7)=28.
Example Question #271 : Algebra
If x must be an integer, which of the following could be the value of f(x)?
f(x) = 2x2 - 6
2
0
4
6
2
If f(x) = 2, then x will be 2. All other times x will yield a radical that cannot be reduced.
Example Question #11 : How To Find F(X)
The cost of a cell phone plan is $40 for the first 100 minutes of calls, and then 5 cents for each minute after. If the variable x is equal to the number of minutes used for calls in a month on that cell phone plan, what is the equation f(x) for the cost, in dollars, of the cell phone plan for calls during that month?
f(x) = 40 + 0.5(x - 100)
f(x) = 40 + 0.5x
f(x) = 40 + 5x
f(x) = 40 + 0.05x
f(x) = 40 + 0.05(x - 100)
f(x) = 40 + 0.05(x - 100)
40 dollars is the constant cost of the cell phone plan, regardless of minute usage for calls. We then add 5 cents, or 0.05 dollars, for every minute of calls over 100. Thus, we do not multiply 0.05 by x, but rather by (x - 100), since the 5 cent charge only applies to minutes used that are over the 100-minute barrier. For example, if you used 101 minutes for calls during the month, you would only pay the 5 cents for that 101st minute, making your cost for calls $40.05. Thus, the answer is 40 + 0.05(x - 100).
Example Question #11 : How To Find F(X)
f(x) = 4x + 2
g(x) = 3x - 1
The two equations above define the functions f(x) = g(x). If f(d) = 2g(d) for some value of d, then what is the value of d?
3/2
-2
2
3
1/2
2
f(x) = 4x + 2
g(x) = 3x - 1
We have f(d) = 2g(d). We multiply each value in g(d) by 2.
4d + 2 = 2(3d - 1) (Distribute the 2 in the parentheses by multiplying each value in them by 2.)
4d + 2 = 6d - 2 (Add 2 to both sides.)
4d + 4 = 6d (Subtract 4d from both sides.)
4 = 2d (Divide both sides by 2.)
2 = d
We can plug that back in to double check.
4(2) + 2 = 6(2) - 2
8 + 2 = 12 - 2
10 = 10
Example Question #271 : Algebra
The function f, where f(x) = x2 + 6x + 8, is related to function g, where g(x) = 5 f(x-2). What is g(3)?
150
175
50
125
75
75
Doing things in an orderly way is a friend to the test-taker.
g(3) = 5 f(3-2)
= 5 f(1)
= 5 [ 12 + 6∙1 + 8]
= 5 [ 1 + 6 + 8]
= 5 [ 15]
= 75
Example Question #11 : How To Find F(X)
Given h(x) = 3x2 – 7. Which of the following values has the highest value?
Explanation: Because of the square in the equation you know the greatest magnitude (absolute value) x value will give you the greatest solution. The greatest magnitude of X listed is -3. Alternatively you could multiple everything out (Solutions: A) 41, B) 17, C) -7, D) 17 E)20)
Example Question #12 : How To Find F(X)
If 2 ≤ |t+1|, which number can it not be?
4
-3
-2
3
-4
-2
Explanation: The values of each answer are A)3 B) 2, C) 1, D)4, E)5.
Example Question #12 : How To Find F(X)
If f(x) = 5x – 10, then what is the value of 5(f(10)) – 10?
50
40
200
190
110
190
The first step is to find what f(10) equals, so f(10)=5(10) – 10 = 40. Then substitute 40 into the second equation: 5(40) – 10 = 200 – 10 = 190.
190 is the correct answer
Example Question #14 : How To Find F(X)
f(x) = 0.1x + 7
g(x) = 1000x + 4
What is g(f(100))?
170040
17004
1700400
1700.4
170.04
17004
First find the value of f(100) = 0.1(100) + 7 = 10 + 7 = 17
Then find g(17) = 1000(17) + 4 = 17000 + 4 = 17004.
Example Question #981 : Algebra
The rate of a gym membership costs p dollars the first month and m dollars per month every month thereafter. Which of the following represents the total cost of the gym membership for n months, if n is a positive integer?
The one-time first-month cost is p, and the monthly cost is m, which gets multipled by every month but the first (of which there are n -1). The total cost is the first-month cost of p, plus the monthly cost for (i.e. times) n -1 months, which makes the total cost equal to p + m (n -1).
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