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Example Questions
Example Question #102 :Algebraic Functions
When we multiply a function by a constant, we multiply each value in the function by that constant. Thus, 2f(x) = 4x + 12. We then subtract g(x) from that function, making sure to distribute the negative sign throughout the function. Subtracting g(x) from 4x + 12 gives us 4x + 12 - (3x - 3) = 4x + 12 - 3x + 3 = x + 15. We then add 2 to x + 15, giving us our answer ofx + 17.
Example Question #103 :Algebraic Functions
Given the following functions, evaluate.
Example Question #104 :Algebraic Functions
The pointis one of the points of intersection of the graphs ofand. Given thatand, find the value of.
Since it’s given than, we know that. We now know that (3, 7) is a point of intersection. Therefore,as well. In other words,, so.
Example Question #105 :Algebraic Functions
Consider these functions:
Which of the following is equivalent to?
Example Question #106 :Algebraic Functions
If, what is the smallest possible value of?
4
12
10
6
8
6
This equation describes a parabola whose vertex is located at the point (4, 6). No matter how large or small the value of t gets, the smallest that f(t) can ever be is 6 because the parabola is concave up. To prove this to yourself you can plug in different values of t and see if you ever get anything smaller than 6.
Example Question #12 :Algebraic Functions
If, then?
To findwhen, we substituteforin.
Thus,.
We expandto.
We can combine like terms to get.
We add 3 to this result to get our final answer.
Example Question #101 :Algebraic Functions
Letandbe functions such that, and. Which of the following is equal to?
Ifandare defined as inverse functions, then. Thus, according to the definition of inverse functions,andgiven in the problem must be inverse functions.
If we want to find the inverse of a function, the most straighforward method is usually replacingwith, swappingand, and then solving for.
We want to find the inverse of. First, we will replacewith.
Next, we will swapand.
Lastly, we will solve for. The equation that we obtain in terms ofwill be in the inverse of, which equals.
We can treatas a proportion,. This allows us to cross multiply and set the results equal to one another.
We want to get y by itself, so let's divide both sides by x.
Next, we will add 3 to both sides.
To combine the right side, we will need to rewrite 3 so that it has a denominator of.
The answer is.
Example Question #108 :Algebraic Functions
.
Example Question #2811 :Sat Mathematics
Let the functionfbe defined byf(x)=x-t. Iff(12)=4, what is the value off(0.5*t)?
First we substitute in 12 for x and set the equation up as 12-t=4. We then get t=8, and substitute that for t and get f(0.5*8), giving us f(4). Plugging 4 in for x, and using t=8 that we found before, gives us:
f(4) = 4 - 8 = -4
Example Question #71 :Algebraic Functions
What is the value of the function f(x) = 6x2+ 16x – 6 when x = –3?
96
–12
–108
0
0
有两种方法可以解决这个问题。第一个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).