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Algebra 1 : Algebraic Functions

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Example Questions

Example Question #1 : How To Find F(X)

A function is given by $f(x)=3x^{2}+3x-4$ . Find f(2) .

Possible Answers:

Correct answer:

Explanation:

Plugging in 2 wherever is present in the formula yields an answer of 14.

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Example Question #1 : How To Find F(X)

If $f(x) = 0.3x^{2}-9x$ , evaluate f(10) .

Possible Answers:

Correct answer:

Explanation:

To solve this function, we simply need to understand that finding f(10) means that x=10 in this specific case. So, we can just substitute 10 in for .

$0.3(10)^{2}=0.3\cdot 100=30$

is equal to , so our final answer is

30-90 or .

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Example Question #3 : How To Find F(X)

In which of these relations is not a function of ?

Possible Answers:

x+y = 1,000,000

$x = y^{2} + 1$

$y = \left | x-100\right |$

xy = 20

$x^{3}y = -1$

Correct answer:

$x = y^{2} + 1$

Explanation:

In the relation $x = y^{2} + 1$ , there are many values of that can be paired with more than one value of - for example, (2,1),(2,-1) .

To demonstrate that is a function of in the other examples, we solve each for :

x+y = 1,000,000 can be rewritten as y = 1,000,000 -x .

$x^{3}y = -1$ can be rewritten as $y = -\frac{1}{x^{3}}$

xy = 20 can be rewritten as $y = \frac{20}{x}$

$y = \left | x-100\right |$ need not be rewritten.

In each case, we see that for any value of , can be uniquely defined.

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Example Question #1 : How To Find F(X)

f(x)= 2x^2 +x+2

$Evaluate\; f(6)$

Possible Answers:

Correct answer:

Explanation:

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Example Question #1 : How To Find F(X)

What is the next number in the following sequence?

10, 20, 25, 50, 55, 110, 115,...

Possible Answers:

120

230

345

130

155

Correct answer:

230

Explanation:

To form this sequence, alternately multiply by 2 and add 5:

$\begin{matrix} 10 \cdot 2 = 20\\ 20+5 = 25\\ 25 \cdot 2 = 50\\ 50 + 5 = 55\\ 55 \cdot 2 = 110 \\ 110 + 5 = 115 \end{matrix}$

To keep the pattern going, double the seventh term to get the eighth:

$115 \cdot 2 = 230$

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Example Question #1 : How To Find F(X)

Define $f (x) = 3 - \sqrt{x-1}$ and $g\left ( x\right ) = 3 + \sqrt{x-1}$

Evaluate $\left (fg \right ) (13)$

Possible Answers:

$\left (fg \right ) (13)$ is undefined.

Correct answer:

Explanation:

$f (x) = 3 - \sqrt{x-1}$

$f (13) = 3 - \sqrt{13-1} = 3 - \sqrt{12}$

$g(x) = 3 + \sqrt{x-1}$

$g(13) = 3 + \sqrt{13-1} = 3 + \sqrt{12}$

The easiest way to find $\left (fg \right ) (13)$ is to take advantage of the fact that the radical expressons are conjugates, and that their product follows the difference of squares pattern.

$fg (13) = f (13) \cdot g (13) = (3 - \sqrt{12}) (3 + \sqrt{12})= 3^{2} - \left (\sqrt{12} \right )^{2} = 9- 12 = -3$

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Example Question #3 : How To Find F(X)

Define $f (x) = 3 - \sqrt{x-1}$ and $g\left ( x\right ) = 3 + \sqrt{x-1}$ .

Evaluate $\left (fg \right ) (-4)$

Possible Answers:

$\left (fg \right ) (-4)$ is undefined.

Correct answer:

$\left (fg \right ) (-4)$ is undefined.

Explanation:

The domain of is the intersection of the domains of the functions and . Both domains are restricted by the same radical expression; since it must hold that the common radicand x-1 is positive:

x-1 > 0 or x > 1

is therefore outside of the domains of and and, subsequently, that of .

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Example Question #4 : How To Find F(X)

What is the next number in the following sequence:

7,8,10,13,17,22,28,...

Possible Answers:

Correct answer:

Explanation:

To get each member of this sequence, add a number that increases by one with each element:

7 + 1 = 8

8+2 = 10

10+3= 13

13+4=17

17+5 = 22

22+6=28

To get the next element, add 7:

28 +7 =35

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Example Question #1 : How To Find F(X)

If g (x) = 5x - 2 , then what is g (3c - 8) ?

Possible Answers:

15c-23

15c-10

15c-38

15c-14

15c-42

Correct answer:

15c-42

Explanation:

Replace with 3c-8 in the definition, then simplify.

g (x) = 5x - 2

$g (3c-8) = 5(3c-8) - 2 = 5 \cdot3c - 5\cdot 8 -2 = 15c -40-2 = 15c - 42$

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Example Question #4 : How To Find F(X)

If g (x) = 3x + 2 , then what is g (2c - 7) ?

Possible Answers:

6c-23

6c -11

6c -5

6c -3

6c-19

Correct answer:

6c-19

Explanation:

Replace with 2c-7 in the definition, then simplify.

g (x) = 3x + 2

$g (2c-7) = 3 (2c-7) + 2 = 3 \cdot 2c-3 \cdot 7 + 2= 6c -21+ 2 = 6c-19$

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Algebra 1 : Algebraic Functions

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Find F(X)

Example Question #1 : How To Find F(X)

Example Question #3 : How To Find F(X)

Example Question #1 : How To Find F(X)

Example Question #1 : How To Find F(X)

Example Question #1 : How To Find F(X)

Example Question #3 : How To Find F(X)

Example Question #4 : How To Find F(X)

Example Question #1 : How To Find F(X)

Example Question #4 : How To Find F(X)

All Algebra 1 Resources

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