Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #3341 : Algebra 1

An infinite sequence begins as follows:

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

Possible Answers:

Correct answer:

Explanation:

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

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

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

Define . Which function is equal to  ?

Possible Answers:

Correct answer:

Explanation:

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

Define  and  .

What is  ?

Possible Answers:

Correct answer:

Explanation:

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

Define  and 

What is  ?

Possible Answers:

Correct answer:

Explanation:

Example Question #15 : Algebraic Functions

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.Function_def

Possible Answers:

Table 4

Table 1

Table 2

None of the above.

Table 3

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.

Example Question #17 : How To Find F(X)

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

A =

B=

C =

D =

Possible Answers:

Set B

Set A and Set B

Set D

Set C

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.

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

Which of the following equations does not represent a function?

Possible Answers:

Correct answer:

Explanation:

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

 

The fact that each value of  gives us two values of   disqualifies it as a function.

Example Question #3351 : Algebra 1

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

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 .

Example Question #3351 : Algebra 1

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

Possible Answers:

x axis

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

origin

All of the above

y axis

Correct answer:

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

Explanation:

Since

It is not symmetric with respect the -axis

It is not symmetric with respect to the -axis

Hence multiplying by  both sides we get

Hence it is not symmetric with respect to the origin.

Example Question #3352 : Algebra 1

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

What is its inverse?

Possible Answers:

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

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

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