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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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Example Questions

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 #1 : 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 #4 : How To Find F(X)

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

Possible Answers:

15c-14

15c-42

15c-10

15c-38

15c-23

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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Example Question #11 : Algebraic Functions

f(x)= x^4-x^3 +7x-5

$Evaluate\; f(-5)$

Possible Answers:

710

460

703

Correct answer:

710

Explanation:

f(-5)= (-5)^4-(-5)^3 +7(-5)-5

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Example Question #12 : Algebraic Functions

An infinite sequence begins as follows:

1, -2, 3, -4, 5, -6, ...

Assuming this pattern continues infinitely, what is the sum of the first one hundred terms?

Possible Answers:

1,275

-5,050

5,050

Correct answer:

Explanation:

This can be best solved by looking at this sum as follows:

(1-2) + (3-4) + (5-6) + (7-8) +...+ (99-100)

= (-1) + (-1) + (-1) + (-1) +...+ (-1)

with taken as an addend fifty times. This is equal to

$-1 \cdot50 = -50$

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Example Question #11 : How To Find F(X)

Define f (x) = 100 - x . Which function is equal to $\left (f \circ f \right )(x)$ ?

Possible Answers:

$\left (f \circ f \right )(x) = x -200$

$\left (f \circ f \right )(x) = 200-x$

$\left (f \circ f \right )(x) = x$

$\left (f \circ f \right )(x) = x + 200$

$\left (f \circ f \right )(x) = 10,000 -200x + x^{2}$

Correct answer:

$\left (f \circ f \right )(x) = x$

Explanation:

$\left (f \circ f \right )(x) = f (f(x)) = f (100 - x) = 100 - (100 -x ) = 100 - 100 + x = x$

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Example Question #11 : How To Find F(X)

Define $f (x) = x ^{2} + x + 1$ and g (x) = x - 3 .

What is (fg) (x) ?

Possible Answers:

$(fg) (x) =x ^{3} + 2x ^{2} +2 x- 3$

$(fg) (x) =x ^{3} - 2x ^{2} +4 x- 3$

$(fg) (x) =x ^{3} - 4x ^{2} - 4 x- 3$

$(fg) (x) =x ^{3} - 2x ^{2} - 2 x- 3$

$(fg) (x) =x ^{3} - 4x ^{2} +4 x- 3$

Correct answer:

$(fg) (x) =x ^{3} - 2x ^{2} - 2 x- 3$

Explanation:

$(fg) (x) = f (x) \cdot g(x)$

$= \left (x ^{2} + x + 1 \right )\left (x-3\right )$

$= \left (x ^{2} + x + 1 \right )x- \left (x ^{2} + x + 1 \right )3$

$=x ^{2}\cdot x + x \cdot x+ 1\cdot x - x ^{2} \cdot 3- x\cdot 3 - 1\cdot 3$

$=x ^{3} + x^{2}+ x - 3x ^{2} - 3 x- 3$

$=x ^{3} + x^{2}- 3x ^{2} + x - 3 x- 3$

$=x ^{3} - 2x ^{2} - 2 x- 3$

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Example Question #12 : How To Find F(X)

Define f(x) = 3x + 4 and $g (x) = x^{2} - x + 5$ .

What is (fg) (x) ?

Possible Answers:

$(fg) (x) = 3x^{3} -4 x^{2} -11x + 20$

$(fg) (x) = 3x^{3} -4x^{2} -11x + 20$

$(fg) (x) = 3x^{3} + 7x^{2} -11x + 20$

$(fg) (x) = 3x^{3} + x^{2} +11x + 20$

$(fg) (x) = 3x^{3} + 7x^{2} +11x + 20$

Correct answer:

$(fg) (x) = 3x^{3} + x^{2} +11x + 20$

Explanation:

$(fg) (x) = f (x) \cdot g(x)$

$= \left (3x + 4 \right )\left (x^{2} - x + 5 \right )$

$= \left (3x + 4 \right ) x^{2} - \left (3x + 4 \right )x +\left (3x + 4 \right ) 5$

$= 3x \cdot x^{2} + 4 \cdot x^{2} - 3x \cdot x - 4 \cdot x +3x\cdot 5 + 4 \cdot 5$

$= 3x^{3} + 4 x^{2} - 3x ^{2} - 4x +15x + 20$

$= 3x^{3} + x^{2} +11x + 20$

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Example Question #13 : How To Find F(X)

Each of the four tables below defines a relationship between (domain) and (range).

One of these tables does not define a function. Identified the table.

Possible Answers:

Table 3

Table 2

Table 1

Table 4

None of the above.

Correct answer:

Table 3

Explanation:

In table 3 we see an value of 3 gets tranformed into 5, 7, 9 ,and 11 which is not possible for a function. Hence the relationship between and in Table 3 does not define a function.

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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

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

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

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

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

Example Question #11 : Algebraic Functions

Example Question #12 : Algebraic Functions

Example Question #11 : How To Find F(X)

Example Question #11 : How To Find F(X)

Example Question #12 : How To Find F(X)

Example Question #13 : How To Find F(X)

All Algebra 1 Resources

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