Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #911 : Functions And Lines

Find the midpoint of the line that contains the following endpoints:

 and 

Possible Answers:

Correct answer:

Explanation:

When finding the midpoint of a line, we use the following formula

where  and  are the endpoints.  

 

Given the points

 and 

we can substitute into the formula.  We get

Example Question #912 : Functions And Lines

Find the midpoint of the line containing the following endpoints:

 and 

Possible Answers:

Correct answer:

Explanation:

When finding the midpoint of a line, we use the following formula

where  and  are the endpoints.  

 

Given the points

 and 

we can substitute into the formula.  We get

Example Question #913 : Functions And Lines

Find the midpoint of the line segment containing the two points 

 and 

Possible Answers:

Correct answer:

Explanation:

To find the midpoint we follow the formula

Plugging in the points  and  for  and 

and we get

Example Question #914 : Functions And Lines

A line is connected by points  and  on a graph.  What is the midpoint?

Possible Answers:

Correct answer:

Explanation:

Write the midpoint formula.

Let  and .

Substitute the given points.

Simplify the coordinate.

The answer is:  

Example Question #915 : Functions And Lines

Find the midpoint between the following two endpoints:  and .

Possible Answers:

Correct answer:

Explanation:

The midpoint formula is . All we need to do is add the x-values and divide by 2, then add the y-values and divide by 2. This leaves us with a midpoint of .

Example Question #1 : How To Find Inverse Variation

Find the inverse of the following function:

 

Possible Answers:

None because the given function is not one-to-one.

Correct answer:

None because the given function is not one-to-one.

Explanation:

which is the same as

If we solve for  we get

Taking the square root of both sides gives us the following:

Interchanging  and  gives us

Which is not one-to-one and therefore not a function.

Example Question #1 : How To Find Inverse Variation

Given

and

.

 

Find .

Possible Answers:

Correct answer:

Explanation:

Starting with

Replace with .

We get the following:

Which is equal to .

Example Question #2 : How To Find Inverse Variation

Given:

and

.

Find .

Possible Answers:

Correct answer:

Explanation:

Start with  which is equal to

and then replace  with . We get the following:

 

which is equal to

Example Question #2 : How To Find Inverse Variation

Which of the following is not a one-to-one function?

Possible Answers:

Correct answer:

Explanation:

Expression 4 is not even a function because for any value of , one gets two values of  violating the definition of a function.  If it is not a function, then it can not be an one-to-one function.

Example Question #5 : How To Find Inverse Variation

 is a one-to-one function specified in terms of a set of  coordinates:

 

A =

 

Which one of the following represents the inverse of the function specified by set A?

B =

C =

D =

E =

F =

Possible Answers:

Set C

Set D

Set B

Set F

Set E

Correct answer:

Set C

Explanation:

The set A is an one-to-one function of the form

One can find   by interchanging the  and  coordinates in set A resulting in set C.

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