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Algebra 1 : Functions and Lines

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Example Question #11 : 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:

5,050

1,275

-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 #12 : Algebraic Functions

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

Possible Answers:

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

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

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

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

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

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 #13 : Algebraic Functions

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

What is (fg) (x) ?

Possible Answers:

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

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

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

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

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

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 #14 : Algebraic Functions

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

What is (fg) (x) ?

Possible Answers:

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

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

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

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

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

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 #3341 : Algebra 1

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 2

None of the above.

Table 3

Table 4

Table 1

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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Example Question #16 : Algebraic Functions

Each of the following 4 sets defines a relationship between and . Which of these four sets defines a one-to-one function:

A = $\left \{ \left ( 1,2 \right )\left ( 2,3 \right )\left ( 3,4 \right )\left ( 4,5 \right ) \right \}$

B= $\left \{ \left ( 1,3 \right )\left ( 2,3 \right )\left ( 3,5 \right )\left ( 4,5 \right ) \right \}$

C = $\left \{ \left ( 1,2 \right )\left ( 2,3 \right )\left ( 2,4 \right )\left ( 2,5 \right )\left ( 6,7\right )\left\right \}$

D = $\left \{ \left ( 1,7 \right )\left ( 2,7 \right )\left ( 3,7 \right )\left ( 4,7 \right ) \right \}$

Possible Answers:

Set A and Set B

Set B

Set C

Set D

Set A

Correct answer:

Set A

Explanation:

Only in set A one can see that there is an unique value of for each value of and similarly each of the values maps into one and only one value. Hence set A must define a one-to-one function.

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Example Question #17 : Algebraic Functions

Which of the following equations does not represent a function?

A) y = 3

B) y = 3x +5

$C) y = -x^{2} + 3$

$D) y^{2} = x^{2}-5$

$E) y = 2^{x}$

Possible Answers:

Correct answer:

Explanation:

The correct answer is equation D. If we solve for we get

$y = \pm \sqrt{x^{2}-5}$

The fact that each value of gives us two values of $\left ( \pm )$ disqualifies it as a function.

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Example Question #1 : Understand Functions: Ccss.Math.Content.8.F.A.1

Which of the following equations represents a one-to-one function:

A) y = 3

B) y = 3x +5

$C) y = 3x^{2}-5$

$D) y^{2}= x^{2} - 5$

E) x = -3

Possible Answers:

Correct answer:

Explanation:

Only equation B maps each value of into a unique value of and in a similar way each and every value of maps into one and only one value of .

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

Test whether the given function is symmetric with respect to the -axis, -axis, origin.

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

Possible Answers:

y axis

All of the above

origin

Not symmetric with respect to x axis, y axis, and the origin

x axis

Correct answer:

Not symmetric with respect to x axis, y axis, and the origin

Explanation:

Since $y = \left ( -x \right )^{3} -\left ( -x \right )^{2} = -x^{3}-x^{2} \neq y$

It is not symmetric with respect the -axis

$-f\left ( x \right ) = -y = -\left ( x^{3}-x^{2} \right ) = -x^{3}+x^{2}\neq f\left ( x \right )$

It is not symmetric with respect to the -axis

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

Hence multiplying by both sides we get

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

Hence it is not symmetric with respect to the origin.

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Example Question #21 : Algebraic Functions

A function is defined by the following set of ordered pairs:

$\left \{ (1,5), (2,4), (3,2), (4,3), (5,5) \right \}$

What is its inverse?

Possible Answers:

$\left \{ (5,1), (4,2), (2,3), (3,4)\right \}$

$\left \{ (1,-5), (2,-4), (3,-2), (4,-3), (5,-5) \right \}$

$\left \{ (5,1), (4,2), (2,3), (3,4), (5,5) \right \}$

$\left \{ (-1,5), (-2,4), (-3,2), (-4,3), (-5,5) \right \}$

The function does not have an inverse.

Correct answer:

The function does not have an inverse.

Explanation:

The inverse of a function is the relation that switches the positions of the coordinates of each ordered pair. However, for a function to have an inverse, the result of those switches must itself be a function. The switches yield the relation

$\left \{ (5,1), (4,2), (2,3), (3,4), (5,5) \right \}$

which is not a function, since the -coordinate 5 is paired with two -coordinates, 1 and 5.

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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #11 : Algebraic Functions

Example Question #12 : Algebraic Functions

Example Question #13 : Algebraic Functions

Example Question #14 : Algebraic Functions

Example Question #3341 : Algebra 1

Example Question #16 : Algebraic Functions

Example Question #17 : Algebraic Functions

Example Question #1 : Understand Functions: Ccss.Math.Content.8.F.A.1

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

Example Question #21 : Algebraic Functions

All Algebra 1 Resources

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